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

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- Aug 20th 2012, 07:41 PMmusngiburgerProving on Perfect Square?
Prove that an integer n is a perfect square if and only if Ƭ (n) is odd.

- Aug 20th 2012, 07:46 PMrichard1234Re: Proving on Perfect Square?
You may want to explain what that T or $\displaystyle \Gamma$ 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 $\displaystyle \Gamma$ since it can easily get confused with the gamma function.

- Aug 20th 2012, 08:59 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 20th 2012, 11:23 PMVlasevRe: Proving on Perfect Square?
The proof of this should be really simple if you recall what the formula for $\displaystyle \tau(n)$ is.