1. ## Perfect Number!!! Help

An integer n is called a perfect number if it equals the sum of all of its positive divisors (excluding itself). For example, 28 is perfect as the divisors of 28 are 1, 2, 4, 7, 14 and 28, and 1 + 2 + 4 + 7 + 14 = 28. Show that if (2^p) − 1 is a prime number, then (2^(p−1))*((2^p) − 1) is a perfect number.

can any one help me?
really stuck
not stuck no idea where to start

2. Originally Posted by AwesomeDesiKid
An integer n is called a perfect number if it equals the sum of all of its positive divisors (excluding itself). For example, 28 is perfect as the divisors of 28 are 1, 2, 4, 7, 14 and 28, and 1 + 2 + 4 + 7 + 14 = 28. Show that if (2^p) − 1 is a prime number, then (2^(p−1))*((2^p) − 1) is a perfect number.

can any one help me?
really stuck
not stuck no idea where to start
Hint: What are the factors of p^2, where p is a prime?
So, in your question what are the factors of (2^(p−1))*((2^p) − 1)?

3. Originally Posted by aman_cc
Hint: What are the factors of p^2, where p is a prime?
So, in your question what are the factors of (2^(p−1))*((2^p) − 1)?
i don't see it
can you explain?

4. Originally Posted by AwesomeDesiKid
i don't see it
can you explain?
From the prime factorization get all the factors of the number. Things will look easy from there.

5. Stronger hint:

$\underbrace{2^0} \cdot \underbrace{ 2^{p-1} \cdot \left(2^p-1 \right)} =\underbrace{ 2^1} \cdot \underbrace{ 2^{p-2} \cdot \left(2^p-1 \right)}= ...$

6. Originally Posted by gmatt
Stronger hint:

$\underbrace{2^0} \cdot \underbrace{ 2^{p-1} \cdot \left(2^p-1 \right)} =\underbrace{ 2^1} \cdot \underbrace{ 2^{p-2} \cdot \left(2^p-1 \right)}= ...$
thanks guys
but i got up to there actually
but thats where im stuckkk

7. Sum up all the factors that you found and prove that they are equal to the original number.

8. Originally Posted by gmatt
Sum up all the factors that you found and prove that they are equal to the original number.
i think i m messing up my summation
cause its not adding up rite

9. show your work so far.

10. Originally Posted by gmatt