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This document contains definitions and examples of several mathematical concepts: 1. It defines leap years as years divisible by 400, or years not divisible by 100 but divisible by 4. 2. It provides the logic/algorithm to determine if a year is a leap year. 3. It provides definitions and examples of prime numbers, Armstrong numbers, perfect numbers, and factorials.

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! " # $ % & ' ! " $ ( ! ) ! * + , - $ ! " ! ! " ! ! # . -- / % 0 ' ( ) 1 . 2 . ! 3 4 * , $ 5 4 - ! " 3 661 0 # 0 %
++++ 7 8 !9 7 8 !9 $ :; < = > :;> :?, # ?;> :?@ ?= ;> A B: C ;D > :? E@ ?= ;> !:;> F ++++ 7 8 !9 7 8 !9 :; < ==#> :;> :?G ! E?;> :?@ ?= ;> :?G ! E@ ?= B ;> :?G ! E@ ?= B ;> :?G ! # !E?;> :?@ @ ?= = #;> :?G ! E@ ?=B#;> :?G ! E@ ?= B:C#;;> !:;> F
6=6=6=6= HHHH ==== HHHH EEEE Definition of leap year: Rule 1: A year is called leap year if it is divisible by 400. For example: 1600, 2000 etc leap year while 1500, 1700 are not leap year. Rule 2: If year is not divisible by 400 as well as 100 but it is divisible by 4 then that year are also leap year. For example: 2004, 2008, 1012 are leap year. Leap year logic or Algorithm of leap year or Condition for leap year: IF year MODULER 400 IS 0 THEN leap_year ELSE IF year MODULER 100 IS 0 THEN not_leap_year ELSE IF year MODULER 4 IS 0 THEN leap_year ELSE not_leap_year ++++ 7 8 !9 :;< > :?, E ?;> :?@ ?= ;> ::: @ AA-; : @ --IA-;;JJ: @ --AA-;; :?@ ?= ;> :?@ ?= ;> -> F E , E - - - -
++++ !!!! " # $" # $" # $" # $ 7 8 !9 7 8 !9 $ :; < > :;> :?, ! ?;> :?@ ?= ;> : 9 ); < :?, # 1 ?;> F :?K , # 1 ?;> !:;> F ++++ &&&& 7 8 !9 7 8 !9 $ :; < = = = = %= $ > :;> :?, ! " ?;> :?@ @ @ @ @ ?= = = = = %;> $ A: C C C C %;D%> : $ 9A*- $ 8A --; :?5 H& ?;> : $ 9A)- $ 8A)*; :?, H& ?;> : $ 9A(- $ 8A(*; :? H& ?;> : $ 9A'- $ 8A'*; :?L H& ?;> : $ 9A%- $ 8A%*; :?3 H& ?;> : $ 9A - $ 8A *; :?MH& ?;> : $ 9A - $ 8A *; :?0H& ?;> !:;>
! " $! " $! " $! " $ 7 8 !9 7 8 !9 7 8 ! !9 $ :; < = > = = > :;> :?G # E?;> :?@ ?= ;> A @ > : AA-; :? ! $ G ?;> :? ! G ?;> !:;> F ++++ ! #! #! #! # #### 7 8 !9 :;< =#= > :?G , # E ?;> :?@ @ @ ?= = #= ;> : H#9- H 9-; :?G & E@ ?= ;> :#H 9-; :?G & # E@ ?=#;> :?G & E@ ?= ;> -> F ++++ ! #! #! #! # 7 8 !9 :;< =#= =# > :?G , # E?;> :?@ @ @ ?= = #= ;>
# A: 9# 9 N E#9 N#E ;> :?G ! # # E@ ?=# ;> -> F ++++%%%% & !& !& !& ! 7 8 !9 7 8 !9 :; < =#= > :;> :?G ! # E?;> :?@ @ @ ?= = #= ;> :: 9#; : 9 ;; :?G ! # # E@ ?= ;> :#9 ; :?G ! # # E@ ?=#;> :?G ! # # E@ ?= ;> !:;> F ++++'''' !!!! 7 8 !9 7 8 !9 :; < =#= > :;> :?G ! # E?;> :?@ @ @ ?= = #= ;> :: 8#; : 8 ;; :?G ! # E@ ?= ;> :#8 ; :?G ! # E@ ?=#;> :?G ! # E@ ?= ;> !:;> F ++++(((( + ,+ ,+ ,+ , 7 8 !9 7 8 !9
7 8 ! !9 $ :; < =#= = = = > :;> :?, =#= ?;> :?@ @ @ ?= = #= ;> A#B#H B B > : 9-; < A:H#C : ;;D: B ;> A:H#H : ;;D: B ;> :? + , E@ @ ?= = ;> F :? ?;> !:;> F !!!! ++++**** $$$$ 7 8 !9 7 8 !9 $ :; < = A-= > :;> :?, ?;> :?@ ?= ;> . ! : 9-; < A @ -> A B -C > A D -> F :? $ E@ ?= ;> !:;> F Definition of Armstrong number or what is an Armstrong number: Definition according to c programming point of view:
Those numbers which sum of the cube of its digits is equal to that number are known as Armstrong numbers. For example 153 since 1^3 + 5^3 + 3^3 = 1+ 125 + 9 =153 Other Armstrong numbers: 370,371,407 etc. In general definition: Those numbers which sum of its digits to power of number of its digits is equal to that number are known as Armstrong numbers. Example 1: 153 Total digits in 153 is 3 And 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153 Example 2: 1634 Total digits in 1634 is 4 And 1^4 + 6^4 + 3^4 +4^4 = 1 + 1296 + 81 + 64 =1634 Examples of Armstrong numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725 ++++ ---- ! " !! " !! " !! " ! 7 8 !9 7 8 !9 :; < = = = > :;> :?G # E?;> :?@ ?= ;> A > A-> . ! : 9-; < A @ -> A C: B B ;> A D ->
F : AA ; :?@ K # ?= ;> :?@ K # ?= ;> !:;> F Definition of prime number: A natural number greater than one has not any other divisors except 1 and itself. In other word we can say which has only two divisors 1 and number itself. For example: 5 Their divisors are 1 and 5. Note: 2 is only even prime number. Logic for prime number in c We will take a loop and divide number from 2 to number/2. If the number is not divisible by any of the numbers then we will print it as prime number. Example of prime numbers : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 etc. ++++ ! " !! " !! " !! " ! 7 8 !9 7 8 !9 $ :; < = = A-> :;> :? # ?;> :?@ ?= ;> . ! :8A ; < : @ AA-; A C >
A C > F : AA ; :? @ % ?= ;> :? @ ?= ;> F !:;> F ++++ ! # . --! # . --! # . --! # . -- DB ! # . --BD 7 8 !9 7 8 !9 $ :; < = A > :;> . ! : 8A --; < A > . ! :8A ; < : @ AA-; # "> CC> F :AA ; :?G @ ?= ;> CC> F !:;> F ++++ ! " . ! ! #! " . ! ! #! " . ! ! #! " . ! ! # 7 8 !9 :;< === = A-= > :?, # E ?;> :?@ ?= ;>
A > . ! : ;< A =A > A @ -> . ! :8A ;< A B > CC> F A C > A D -> F : AA ; :?@ # ?= ;> :?@ # ?= ;> -> F E , # E % % # + ! " !+ ! " !+ ! " !+ ! " ! 7 8 !9 7 8 !9 $ :; < ="A = > :;> :? # ?;> :?@ ?= ;> . ! : 8-; < : @ "AA-; "CC> F : AA"; :? ?;>
:? ?;> !:;> F ++++ # . --# . --# . --# . -- 7 8 !9 7 8 !9 $ :; < = A > :;> . ! : 8A --; < A > . ! :8A ; < : @ AA-; # "> CC> F :AA ; :?G @ ?= ;> CC> F !:;> F ++++ //// 7 8 !9 7 8 !9 $ :; < = > > :;> :?G # E?;> :?@ ?= ;> A-> . ! : 9-; < A @ -> A C >
A D -> F :? ! E@ ?= ;> !:;> F ++++ Factorial of number is defined as: Factorial (n) = 1*2*3 … * n For example: Factorial of 5 = 1*2*3*4*5 = 120 Note: Factorial of zero = 1 ++++ 0000 7 8 !9 7 8 !9 :; < == > :;> :?G # ?;> :?@ ?= ;> A > A > . ! :9-; < A B > HH> F :? ! @ E@ ?= =;> !:;> F Definition of Palindrome number or what is palindrome number? A number is called palindrome number if it is remain same when its digits are reversed. For example 121 is palindrome number. When we will reverse its digit it will remain same number i.e. 121 Palindrome numbers examples: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191 etc.
++++ 7 8 !9 7 8 !9 :; < = = = > :;> :?G # ?;> :?@ ?= ;> A > A-> . ! : 9-; < A @ -> A C: B B ;> A D -> F : AA ; :?@ K O # ?= ;> :?@ K # ?= ;> !:;> F Definition of perfect number or what is perfect number? Perfect number is a positive number which sum of all positive divisors excluding that number is equal to that number. For example 6 is perfect number since divisor of 6 are 1, 2 and 3. Sum of its divisor is 1 + 2+ 3 =6 Note: 6 is the smallest perfect number. Next perfect number is 28 since 1+ 2 + 4 + 7 + 14 = 28 Some more perfect numbers: 496, 8128
++++ 7 8 !9 7 8 !9 :; < == > :;> :?G # ?;> :?@ ?= ;> A > A-> . ! :8 ; < : @ AA-; A C > CC> F : AA ; :?@ K # ?= ;> :?@ K # ?= ;> !:;> F OOOO MMMM HHHH !!!! ++++ ! "! "! "! " 7 8 !9 7 8 !9 $ :; < = A-= > :;> :? ! ?;> :?@ ?= ;> < A @ -> A B -C > A D -> F . ! : 9-;> :? ?;> : AA ;
< :? E@ ?= ;> F !:;> F ++++ ! "! "! "! " 7 8 !9 7 8 !9 $ :; < ="A > :;> :? ?;> :?@ ?= ;> < : @ "AA-; < :?6 ?;> P :-;> F "CC> F . ! :"8 ;> :? ?;> !:;> F ++++ $$$$ 7 8 !9 7 8 !9 $ :; < = A-= > :? ! ?;> :?@ ?= ;> < A @ -> A B -C > A D -> F
. ! : 9-;> :? ! $ E@ ?= ;> !:;> F ++++ $$$$ 7 8 !9 7 8 !9 7 8 ! !9 $ :; < = = A-= A =PA = > :;> :?, ! ?;> :?@ ?= ;> :?, . ! ! # $ ?;> :?@ ?= ;> < A @ -> :?@ ?=;> A C > A B > A D -> PCC> F . ! :P8A ;> :?G E@ ?= ;> :?G Q E@ ?= ;> !:;> F . !. !. !. !HHHH3333 ++++ 1 .1 .1 .1 . 2222 . ! 3 4. ! 3 4. ! 3 4. ! 3 4 7 8 !9 7 8 !9 $ :; < ! !> :;> :?G ! E?;> :?@ ?= !;>
. !: !; < R RE :?@ $ . ?= !;> # "> R, RE :?@ $ . ?= !;> # "> R6RE :?@ $ . ?= !;> # "> R5 RE :?@ $ . ?= !;> # "> RO RE :?@ $ . ?= !;> # "> E :?@ $ . ?;> F !:;> F ++++ , $ 5 4, $ 5 4, $ 5 4, $ 5 4 7 8 !9 :; < #> :2 K # 4;> :2@ 4= #;> . !: # @ ; < - E :? ! # @ $ G ?= #;> E :? ! # @ G ?= #;> # "> F F
0000 HHHHSSSS ++++ 7 8 !9 :;< > T = PT > :?, ! . E ?;> :?@ ?= T ;> :?, ! ! ! E ?;> :?@ ?= PT ;> :?S $ E ?;> : A T > 8A PT > CC;< ::: @ AA-; : @ --IA-;;JJ: @ --AA-;; :?@ ?= ;> F -> } + ! "+ ! "+ ! "+ ! " 3 6613 6613 6613 661 7 8 !9 7 8 !9 $ :; < > :;> :A'%> 8A*-> CC; :?G @ A@ ?==;> !:;> F ++++ 0 #0 #0 #0 # 7 8 !9 7 8 !9 $ :; < = A-= #A == > :;> :? # ?;>
:?@ ?= ;> :A-> 8A > CC; < A > A #> #A C > :?@ ?= #;> F !:;> F + 3 # --+ 3 # --+ 3 # --+ 3 # -- 7 8 !9 :;< == > = P> :?, ! E ?;> :?@ ?= ;> :?, ! P E ?;> :?@ ?= P;> :? # $ E ?;> : A > 8A P> CC;< A > A -> . ! :8 ;< : @ AA-; A C > CC> F : AA ; :?@ ?= ;> F -> F Sample output: Enter the minimum range: 1 , ! P E - # $ E '
++++ ---- ! " !! " !! " !! " ! 7 8 !9 :;< = = = > = P> :?, ! E ?;> :?@ ?= ;> :?, ! P E ?;> :?@ ?= P;> :? # $ E ?;> : A > 8A P> CC;< A > A -> . ! : IA-;< A @ -> A D -> A C: B B ;> F : AA ; :?@ ?= ;> F -> F ++++ BBBB BBBBBBBB BBBBBBBBBBBB BBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB 7 8 !9 7 8 !9 $ :; < = =U>
:;> :? # ?;> :?@ ?= ;> :A-> 8A > CC; < :UA->U8A >UCC; < :?B?;> F :?G ?;> F !:;> F ++++ BBBB BBBBBBBB BBBBBBBBBBBB BBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBB BBBBBBBBBBBB BBBBBBBB BBBB 7 8 !9 7 8 !9 $ :; < = =U> :;> :? # ?;> :?@ ?= ;> :UA >U8A >UCC; < :A > 8AU> CC; < :?B?;> F :?G ?;>
F :UA >U9A->UHH; < :AU> 9A > HH; < :?B?;> F :?G ?;> F !:;> F ++++ 7 8 !9 7 8 !9 $ :; < = =U> :;> :? # ?;> :?@ ?= ;> :UA >U8A >UCC; < :A > 8AU> CC; < :?@ ?=;> F :?G ?;> F :UA >U9A->UHH; < :AU> 9A > HH; <
:?@ ?=;> F :?G ?;> F !:;> F ++++ program to display ASCII values 7 8 !9 :;< > :A-> 8A %%> CC; :? 3 66$ ! @ E @ G ?==;> -> F ++++ 0000 7 8 !9 :;< =U= ="A > :?, ! E ?;> :?@ ?= ;> :?0S5 VMR 6 K & S, G G ?;> :A > 8A > CC;< :UA >U8A >UCC="CC; :? @ ?=";> :?G ?;> F -> F E , ! E -
0S5 VMR 6 K & S, % ' ( ) * - % ' ( ) * - % ' ( ) * - % ' ( ) * - % ' ( ) * %- % % % % %% ++++ 3333 7 8 !9 :;< ==U="> :?, ! ?;> :?@ ?= ;> :A > 8A > CC;< :UA >U8A H >UCC; :? ?;> :"A >"8 >"CC; :?@ ?=";> :"A >"9A >"HH; :?@ ?=";> :?G ?;> F -> F ++++ 3333 B BBB BBBBB
BBBBBBB BBBBBBBBB 7 8 !9 :; < . = = = > :?, ! # . . ! ?;> :?@ ?= ;> A > : . A > . 8A > . CC ; < : A > 8 > CC ; :? ?;> HH> : A > 8A B . H > CC ; :?B?;> :?G ?;> F -> F ++++ 3333 A B C D E F G H A B C D E F G A B C D E F A B C D E A B C D A B C
A B A 7 8 !9 :; < ! ! A R R> = ="= A -> :?@ ?= ;> :" A > " 9A > "HH ; < : A > 8A > CC; :? ?;> CC> : A > 8A " > CC ; < :?@ ?= !;> !CC> F :?G ?;> ! A R R> F -> F ++++ 3333 1 01 010 1010 10101 7 8 !9 :; < = ="= A > :?@ ?= ;> : A > 8A > CC ;
< :" A > " 8A > "CC ; < :?@ ?= ;> : AA - ; A > A -> F :?G ?;> F -> F ++++ 3333 p pr pro prog progr progra program 7 8 !9 7 8 !9 :; < ! W --X> ="= !> :?, G ?;> : ;> ! A : ;> : A - > 8 ! > CC ; < :" A - > " 8A > "CC ; < :?@ ?= W"X;> F :?G ?;> F -> F
++++ 3333 1 121 12321 1234321 123454321 7 8 !9 :; < = ="=P A > :?@ ?= ;> : A > 8A > CC ; < :" A > " 8A > "CC ; < :?@ ?=P;> PCC> F PHH> :" A > " 8A H > "CC ; < PHH> :?@ ?=P;> F :?G ?;> P A > F -> F ++++ 3333 $ !$ !$ !$ ! DBBBBBBBB APCPY D ICPY D IC PY D IBD 7 8 !9 7 8 !9 7 8 ! !9 $ :; < A ==P== > > :;>
:?, ! $ ?;> :?@ ?= ;> :?, ! $ P?;> :?@ ?= P;> AP> :A > 8A > CA ; < A > :A > 8A > CC; A B > A C . :P=;D> F :?G E@ ?= ;> !:;> F ++++ 3333 $ !$ !$ !$ ! DBBBBBBBB A D Y C D Y C D Y CCCCCCCCCCC D Y BD 7 8 !9 7 8 !9 7 8 ! !9 $ :; < == > P= > :;> :?, ! $ ?;> :?@ ?= ;> :A > 8A > CC; < PAPC . := ;> A C . := ;> F :?G PE@ =G E@ ?=P= ;> !:;> F
ZO Q 3 5 K 5 SZO Q 3 5 K 5 SZO Q 3 5 K 5 SZO Q 3 5 K 5 SHHHH 3 5 K 6K O , E3 5 K 6K O , E3 5 K 6K O , E3 5 K 6K O , E HHHH 7 8 !9 7 8 !9 7 8 ! !9 $ :; < == > P= > :;> :A > 8A -> CC; < :@ AA-; > :?G @ ?=;> F !:;> F & 5 5& 5 5& 5 5& 5 5 EEEE HHHH 7 8 !9 7 8 !9 7 8 ! !9 $ :; < = = A-> :;> :?, ! $ ?;> :?@ ?= ;> $E : AA-; :?@ ?= ;> < A @ -> A B -C > A D -> $> F !:;> F & 5 5& 5 5& 5 5& 5 5 EEEE HHHH 7 8 !9 7 8 !9 7 8 ! !9 $ :; <
> :;> :?, ! $ ?;> :?@ ?= ;> : @ AA-; $ > > $ E :?, $ ?;> > E :? ?;> E :?G @ ?= ;> !:;> F

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Progr1

  • 1.
    ! " #$ % & ' ! " $ ( ! ) ! * + , - $ ! " ! ! " ! ! # . -- / % 0 ' ( ) 1 . 2 . ! 3 4 * , $ 5 4 - ! " 3 661 0 # 0 %
  • 2.
    ++++ 7 8 !9 78 !9 $ :; < = > :;> :?, # ?;> :?@ ?= ;> A B: C ;D > :? E@ ?= ;> !:;> F ++++ 7 8 !9 7 8 !9 :; < ==#> :;> :?G ! E?;> :?@ ?= ;> :?G ! E@ ?= B ;> :?G ! E@ ?= B ;> :?G ! # !E?;> :?@ @ ?= = #;> :?G ! E@ ?=B#;> :?G ! E@ ?= B:C#;;> !:;> F
  • 3.
    6=6=6=6= HHHH ====HHHH EEEE Definition of leap year: Rule 1: A year is called leap year if it is divisible by 400. For example: 1600, 2000 etc leap year while 1500, 1700 are not leap year. Rule 2: If year is not divisible by 400 as well as 100 but it is divisible by 4 then that year are also leap year. For example: 2004, 2008, 1012 are leap year. Leap year logic or Algorithm of leap year or Condition for leap year: IF year MODULER 400 IS 0 THEN leap_year ELSE IF year MODULER 100 IS 0 THEN not_leap_year ELSE IF year MODULER 4 IS 0 THEN leap_year ELSE not_leap_year ++++ 7 8 !9 :;< > :?, E ?;> :?@ ?= ;> ::: @ AA-; : @ --IA-;;JJ: @ --AA-;; :?@ ?= ;> :?@ ?= ;> -> F E , E - - - -
  • 4.
    ++++ !!!! "# $" # $" # $" # $ 7 8 !9 7 8 !9 $ :; < > :;> :?, ! ?;> :?@ ?= ;> : 9 ); < :?, # 1 ?;> F :?K , # 1 ?;> !:;> F ++++ &&&& 7 8 !9 7 8 !9 $ :; < = = = = %= $ > :;> :?, ! " ?;> :?@ @ @ @ @ ?= = = = = %;> $ A: C C C C %;D%> : $ 9A*- $ 8A --; :?5 H& ?;> : $ 9A)- $ 8A)*; :?, H& ?;> : $ 9A(- $ 8A(*; :? H& ?;> : $ 9A'- $ 8A'*; :?L H& ?;> : $ 9A%- $ 8A%*; :?3 H& ?;> : $ 9A - $ 8A *; :?MH& ?;> : $ 9A - $ 8A *; :?0H& ?;> !:;>
  • 5.
    ! " $!" $! " $! " $ 7 8 !9 7 8 !9 7 8 ! !9 $ :; < = > = = > :;> :?G # E?;> :?@ ?= ;> A @ > : AA-; :? ! $ G ?;> :? ! G ?;> !:;> F ++++ ! #! #! #! # #### 7 8 !9 :;< =#= > :?G , # E ?;> :?@ @ @ ?= = #= ;> : H#9- H 9-; :?G & E@ ?= ;> :#H 9-; :?G & # E@ ?=#;> :?G & E@ ?= ;> -> F ++++ ! #! #! #! # 7 8 !9 :;< =#= =# > :?G , # E?;> :?@ @ @ ?= = #= ;>
  • 6.
    # A: 9#9 N E#9 N#E ;> :?G ! # # E@ ?=# ;> -> F ++++%%%% & !& !& !& ! 7 8 !9 7 8 !9 :; < =#= > :;> :?G ! # E?;> :?@ @ @ ?= = #= ;> :: 9#; : 9 ;; :?G ! # # E@ ?= ;> :#9 ; :?G ! # # E@ ?=#;> :?G ! # # E@ ?= ;> !:;> F ++++'''' !!!! 7 8 !9 7 8 !9 :; < =#= > :;> :?G ! # E?;> :?@ @ @ ?= = #= ;> :: 8#; : 8 ;; :?G ! # E@ ?= ;> :#8 ; :?G ! # E@ ?=#;> :?G ! # E@ ?= ;> !:;> F ++++(((( + ,+ ,+ ,+ , 7 8 !9 7 8 !9
  • 7.
    7 8 !!9 $ :; < =#= = = = > :;> :?, =#= ?;> :?@ @ @ ?= = #= ;> A#B#H B B > : 9-; < A:H#C : ;;D: B ;> A:H#H : ;;D: B ;> :? + , E@ @ ?= = ;> F :? ?;> !:;> F !!!! ++++**** $$$$ 7 8 !9 7 8 !9 $ :; < = A-= > :;> :?, ?;> :?@ ?= ;> . ! : 9-; < A @ -> A B -C > A D -> F :? $ E@ ?= ;> !:;> F Definition of Armstrong number or what is an Armstrong number: Definition according to c programming point of view:
  • 8.
    Those numbers whichsum of the cube of its digits is equal to that number are known as Armstrong numbers. For example 153 since 1^3 + 5^3 + 3^3 = 1+ 125 + 9 =153 Other Armstrong numbers: 370,371,407 etc. In general definition: Those numbers which sum of its digits to power of number of its digits is equal to that number are known as Armstrong numbers. Example 1: 153 Total digits in 153 is 3 And 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153 Example 2: 1634 Total digits in 1634 is 4 And 1^4 + 6^4 + 3^4 +4^4 = 1 + 1296 + 81 + 64 =1634 Examples of Armstrong numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725 ++++ ---- ! " !! " !! " !! " ! 7 8 !9 7 8 !9 :; < = = = > :;> :?G # E?;> :?@ ?= ;> A > A-> . ! : 9-; < A @ -> A C: B B ;> A D ->
  • 9.
    F : AA ; :?@K # ?= ;> :?@ K # ?= ;> !:;> F Definition of prime number: A natural number greater than one has not any other divisors except 1 and itself. In other word we can say which has only two divisors 1 and number itself. For example: 5 Their divisors are 1 and 5. Note: 2 is only even prime number. Logic for prime number in c We will take a loop and divide number from 2 to number/2. If the number is not divisible by any of the numbers then we will print it as prime number. Example of prime numbers : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 etc. ++++ ! " !! " !! " !! " ! 7 8 !9 7 8 !9 $ :; < = = A-> :;> :? # ?;> :?@ ?= ;> . ! :8A ; < : @ AA-; A C >
  • 10.
    A C > F :AA ; :? @ % ?= ;> :? @ ?= ;> F !:;> F ++++ ! # . --! # . --! # . --! # . -- DB ! # . --BD 7 8 !9 7 8 !9 $ :; < = A > :;> . ! : 8A --; < A > . ! :8A ; < : @ AA-; # "> CC> F :AA ; :?G @ ?= ;> CC> F !:;> F ++++ ! " . ! ! #! " . ! ! #! " . ! ! #! " . ! ! # 7 8 !9 :;< === = A-= > :?, # E ?;> :?@ ?= ;>
  • 11.
    A > . !: ;< A =A > A @ -> . ! :8A ;< A B > CC> F A C > A D -> F : AA ; :?@ # ?= ;> :?@ # ?= ;> -> F E , # E % % # + ! " !+ ! " !+ ! " !+ ! " ! 7 8 !9 7 8 !9 $ :; < ="A = > :;> :? # ?;> :?@ ?= ;> . ! : 8-; < : @ "AA-; "CC> F : AA"; :? ?;>
  • 12.
    :? ?;> !:;> F ++++ #. --# . --# . --# . -- 7 8 !9 7 8 !9 $ :; < = A > :;> . ! : 8A --; < A > . ! :8A ; < : @ AA-; # "> CC> F :AA ; :?G @ ?= ;> CC> F !:;> F ++++ //// 7 8 !9 7 8 !9 $ :; < = > > :;> :?G # E?;> :?@ ?= ;> A-> . ! : 9-; < A @ -> A C >
  • 13.
    A D -> F :?! E@ ?= ;> !:;> F ++++ Factorial of number is defined as: Factorial (n) = 1*2*3 … * n For example: Factorial of 5 = 1*2*3*4*5 = 120 Note: Factorial of zero = 1 ++++ 0000 7 8 !9 7 8 !9 :; < == > :;> :?G # ?;> :?@ ?= ;> A > A > . ! :9-; < A B > HH> F :? ! @ E@ ?= =;> !:;> F Definition of Palindrome number or what is palindrome number? A number is called palindrome number if it is remain same when its digits are reversed. For example 121 is palindrome number. When we will reverse its digit it will remain same number i.e. 121 Palindrome numbers examples: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191 etc.
  • 14.
    ++++ 7 8 !9 78 !9 :; < = = = > :;> :?G # ?;> :?@ ?= ;> A > A-> . ! : 9-; < A @ -> A C: B B ;> A D -> F : AA ; :?@ K O # ?= ;> :?@ K # ?= ;> !:;> F Definition of perfect number or what is perfect number? Perfect number is a positive number which sum of all positive divisors excluding that number is equal to that number. For example 6 is perfect number since divisor of 6 are 1, 2 and 3. Sum of its divisor is 1 + 2+ 3 =6 Note: 6 is the smallest perfect number. Next perfect number is 28 since 1+ 2 + 4 + 7 + 14 = 28 Some more perfect numbers: 496, 8128
  • 15.
    ++++ 7 8 !9 78 !9 :; < == > :;> :?G # ?;> :?@ ?= ;> A > A-> . ! :8 ; < : @ AA-; A C > CC> F : AA ; :?@ K # ?= ;> :?@ K # ?= ;> !:;> F OOOO MMMM HHHH !!!! ++++ ! "! "! "! " 7 8 !9 7 8 !9 $ :; < = A-= > :;> :? ! ?;> :?@ ?= ;> < A @ -> A B -C > A D -> F . ! : 9-;> :? ?;> : AA ;
  • 16.
    < :? E@ ?=;> F !:;> F ++++ ! "! "! "! " 7 8 !9 7 8 !9 $ :; < ="A > :;> :? ?;> :?@ ?= ;> < : @ "AA-; < :?6 ?;> P :-;> F "CC> F . ! :"8 ;> :? ?;> !:;> F ++++ $$$$ 7 8 !9 7 8 !9 $ :; < = A-= > :? ! ?;> :?@ ?= ;> < A @ -> A B -C > A D -> F
  • 17.
    . ! :9-;> :? ! $ E@ ?= ;> !:;> F ++++ $$$$ 7 8 !9 7 8 !9 7 8 ! !9 $ :; < = = A-= A =PA = > :;> :?, ! ?;> :?@ ?= ;> :?, . ! ! # $ ?;> :?@ ?= ;> < A @ -> :?@ ?=;> A C > A B > A D -> PCC> F . ! :P8A ;> :?G E@ ?= ;> :?G Q E@ ?= ;> !:;> F . !. !. !. !HHHH3333 ++++ 1 .1 .1 .1 . 2222 . ! 3 4. ! 3 4. ! 3 4. ! 3 4 7 8 !9 7 8 !9 $ :; < ! !> :;> :?G ! E?;> :?@ ?= !;>
  • 18.
    . !: !; < RRE :?@ $ . ?= !;> # "> R, RE :?@ $ . ?= !;> # "> R6RE :?@ $ . ?= !;> # "> R5 RE :?@ $ . ?= !;> # "> RO RE :?@ $ . ?= !;> # "> E :?@ $ . ?;> F !:;> F ++++ , $ 5 4, $ 5 4, $ 5 4, $ 5 4 7 8 !9 :; < #> :2 K # 4;> :2@ 4= #;> . !: # @ ; < - E :? ! # @ $ G ?= #;> E :? ! # @ G ?= #;> # "> F F
  • 19.
    0000 HHHHSSSS ++++ 7 8!9 :;< > T = PT > :?, ! . E ?;> :?@ ?= T ;> :?, ! ! ! E ?;> :?@ ?= PT ;> :?S $ E ?;> : A T > 8A PT > CC;< ::: @ AA-; : @ --IA-;;JJ: @ --AA-;; :?@ ?= ;> F -> } + ! "+ ! "+ ! "+ ! " 3 6613 6613 6613 661 7 8 !9 7 8 !9 $ :; < > :;> :A'%> 8A*-> CC; :?G @ A@ ?==;> !:;> F ++++ 0 #0 #0 #0 # 7 8 !9 7 8 !9 $ :; < = A-= #A == > :;> :? # ?;>
  • 20.
    :?@ ?= ;> :A->8A > CC; < A > A #> #A C > :?@ ?= #;> F !:;> F + 3 # --+ 3 # --+ 3 # --+ 3 # -- 7 8 !9 :;< == > = P> :?, ! E ?;> :?@ ?= ;> :?, ! P E ?;> :?@ ?= P;> :? # $ E ?;> : A > 8A P> CC;< A > A -> . ! :8 ;< : @ AA-; A C > CC> F : AA ; :?@ ?= ;> F -> F Sample output: Enter the minimum range: 1 , ! P E - # $ E '
  • 21.
    ++++ ---- !" !! " !! " !! " ! 7 8 !9 :;< = = = > = P> :?, ! E ?;> :?@ ?= ;> :?, ! P E ?;> :?@ ?= P;> :? # $ E ?;> : A > 8A P> CC;< A > A -> . ! : IA-;< A @ -> A D -> A C: B B ;> F : AA ; :?@ ?= ;> F -> F ++++ BBBB BBBBBBBB BBBBBBBBBBBB BBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB 7 8 !9 7 8 !9 $ :; < = =U>
  • 22.
    :;> :? # ?;> :?@?= ;> :A-> 8A > CC; < :UA->U8A >UCC; < :?B?;> F :?G ?;> F !:;> F ++++ BBBB BBBBBBBB BBBBBBBBBBBB BBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBB BBBBBBBBBBBB BBBBBBBB BBBB 7 8 !9 7 8 !9 $ :; < = =U> :;> :? # ?;> :?@ ?= ;> :UA >U8A >UCC; < :A > 8AU> CC; < :?B?;> F :?G ?;>
  • 23.
    F :UA >U9A->UHH; < :AU> 9A> HH; < :?B?;> F :?G ?;> F !:;> F ++++ 7 8 !9 7 8 !9 $ :; < = =U> :;> :? # ?;> :?@ ?= ;> :UA >U8A >UCC; < :A > 8AU> CC; < :?@ ?=;> F :?G ?;> F :UA >U9A->UHH; < :AU> 9A > HH; <
  • 24.
    :?@ ?=;> F :?G ?;> F !:;> F ++++program to display ASCII values 7 8 !9 :;< > :A-> 8A %%> CC; :? 3 66$ ! @ E @ G ?==;> -> F ++++ 0000 7 8 !9 :;< =U= ="A > :?, ! E ?;> :?@ ?= ;> :?0S5 VMR 6 K & S, G G ?;> :A > 8A > CC;< :UA >U8A >UCC="CC; :? @ ?=";> :?G ?;> F -> F E , ! E -
  • 25.
    0S5 VMR 6K & S, % ' ( ) * - % ' ( ) * - % ' ( ) * - % ' ( ) * - % ' ( ) * %- % % % % %% ++++ 3333 7 8 !9 :;< ==U="> :?, ! ?;> :?@ ?= ;> :A > 8A > CC;< :UA >U8A H >UCC; :? ?;> :"A >"8 >"CC; :?@ ?=";> :"A >"9A >"HH; :?@ ?=";> :?G ?;> F -> F ++++ 3333 B BBB BBBBB
  • 26.
    BBBBBBB BBBBBBBBB 7 8 !9 :; < .= = = > :?, ! # . . ! ?;> :?@ ?= ;> A > : . A > . 8A > . CC ; < : A > 8 > CC ; :? ?;> HH> : A > 8A B . H > CC ; :?B?;> :?G ?;> F -> F ++++ 3333 A B C D E F G H A B C D E F G A B C D E F A B C D E A B C D A B C
  • 27.
    A B A 7 8!9 :; < ! ! A R R> = ="= A -> :?@ ?= ;> :" A > " 9A > "HH ; < : A > 8A > CC; :? ?;> CC> : A > 8A " > CC ; < :?@ ?= !;> !CC> F :?G ?;> ! A R R> F -> F ++++ 3333 1 01 010 1010 10101 7 8 !9 :; < = ="= A > :?@ ?= ;> : A > 8A > CC ;
  • 28.
    < :" A >" 8A > "CC ; < :?@ ?= ;> : AA - ; A > A -> F :?G ?;> F -> F ++++ 3333 p pr pro prog progr progra program 7 8 !9 7 8 !9 :; < ! W --X> ="= !> :?, G ?;> : ;> ! A : ;> : A - > 8 ! > CC ; < :" A - > " 8A > "CC ; < :?@ ?= W"X;> F :?G ?;> F -> F
  • 29.
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  • 30.
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  • 31.
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  • 32.
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