Thread: Abundant Proof

I do not know where to start Please HELP!!

Prove that any multiple of a perfect number is abundant.

Originally Posted by aubre18

I do not know where to start Please HELP!!

Prove that any multiple of a perfect number is abundant.

What is the definition of "perfect number"? What is the definition of "abundant number"? If it is not clear, try some simple examples. The smallest perfect number is 6. It is "perfect" because its proper divisors are 1, 2, and 3 and those add to 6. Okay, multiply 6 by p. 1, 2, and 3 are still proper divisors. So are p, 2p and 3p. Those three alone add to 6p!