Amicable numbers are pairs of numbers where the sum of the divisors of each number (excluding the number itself) is equal to the other number. The document provides examples of amicable number pairs such as 220 and 284, where the sum of divisors of 220 is 284 and the sum of divisors of 284 is 220. The document also explains how to find if two numbers are an amicable pair by listing the divisors of each number and comparing the sums. Amicable numbers were first discovered in antiquity by Pythagoras and later, in 1636, Fermat discovered another pair.

1. Amicable Numbers

2. How to find out pairs of
Amicable Numbers
One of the most beautiful concepts
from maths constituts the “Amicable
Numbers”
But what are ‘Amicable numbers’ ?
DEFINITION: Each number is equal
with the sum of the divizors of the other
number including 1 and excluding the
number itself (like divizors)
Examples of amicable numbers: 220
and 284, 1184 and 1210, 2620 and 2924.

3. The first amicable numbers were
discovered in antiquity.
Examples for finding out pairs of amicable
numbers:
D220={1,2,4,5,10,11,20,22,44,55,110,220}
1+2+4+5+10+11+20+22+44+55+110=284
D284={1,2,4,7,71,142,284}
1+2+4+7+71+142=220
=> 220 and 284= amicable
numbers

4. .
D1184={1,2,4,8,16,32,37,74,148,296,592}
1+2+4+8+16+32+37+74+148+296+592=1210
D1210={1,2,5,10,11,22,55,110,121,242,605}
1+2+5+10+11+22+55+110+121+242+605=1184
=> 1184 and 1210= amicable numbers

5. O PITAGORA was the first who
discovered the first pair of amicable
numbers [220 and 284]
O Much later, in 1636, PIERRE FERMAT
discovered the second pair of amicable
numbers (17296 and 18416)

6. BIBLIOGRAPHY
O http://desprenumere.blogspot.ro/2012/12nu
muere-prietene.html
O http://ro.wikipedia.org/wiki/Numere_prieten
e
O http://en.wikipedia.org/wiki/Amicable_numb
ers
O http://mathworld.wolfram.com/AmicablePair
.html
O http://www.numbergossip.com/list#amicable
_numbers