A perfect number is a positive integer equal to the sum of its positive divisors excluding the number itself. For example, 6 is perfect because 1 + 2 + 3 = 6. Equivalently, a number is perfect if the sum of all its divisors including itself is twice the number. The earliest known discussion of perfect numbers was by Euclid, who proved that if 2^p - 1 is prime, then 2^(p-1)(2^p - 1) is perfect. Euler later proved all even perfect numbers have this form.

1. PERFECT NUMBERS
ALAN S. ABERILLA

2. In number theory, a perfect number is a positive
integer that is equal to the sum of its positive divisors,
excluding the number itself. For instance, 6 has
divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 =
6, so 6 is a perfect number.
The sum of divisors of a
number excluding the number
itself, is called aliquot
sum, so a perfect number is one that is equal to its
aliquot sum.

3. Equivalently, a perfect number is a number that is half
the the sum of all of its positive divisors including
itself; in symbols, σ1(n) = 2n where σ1 is the
sum-of-divisors function. For instance, 28 is perfect as 1
+ 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28.
This definition is ancient, appearing as early as Euclid’s
Elements (VII.22) where it is called τέλειος
ἀριθμός (perfect, ideal, or complete number). Euclid also
proved a formation rule (IX.36) whereby is an even
perfect number whenever is a prime of the form for
prime - what is now called a Mersenne prime. Two
millennia later, Euler proved that all even perfect
numbers are of this form. This is known as the Euclid-
Euler Theorem.

4. ACTIVITY 5:
1. Make an illustration a perfect number 28.
2. Give the aliquot sum of 496
Use short bond paper (handwritten or
computerized) – utilize the folder of assignment
1