Prove that an integer n is a perfect square if and only if Ƭ (n) is odd.

Printable View

- Aug 20th 2012, 08:41 PMmusngiburgerProving on Perfect Square?
Prove that an integer n is a perfect square if and only if Ƭ (n) is odd.

- Aug 20th 2012, 08:46 PMrichard1234Re: Proving on Perfect Square?
You may want to explain what that T or symbol is. If it refers to the number of positive integer divisors of n (usually denoted d(n)), the statement is true. I doubt it would be a since it can easily get confused with the gamma function.

- Aug 20th 2012, 09:59 PMmusngiburgerRe: Proving on Perfect Square?
Sorry about that. Ƭ (n) is supposed to be total number of positive divisors of n where n>0.

- Aug 21st 2012, 12:23 AMVlasevRe: Proving on Perfect Square?
The proof of this should be really simple if you recall what the formula for is.