# Thread: Proving on Perfect Square?

1. ## Proving on Perfect Square?

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

2. ## Re: Proving on Perfect Square?

You may want to explain what that T or $\Gamma$ 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 $\Gamma$ since it can easily get confused with the gamma function.

3. ## Re: Proving on Perfect Square?

Sorry about that. Ƭ (n) is supposed to be total number of positive divisors of n where n>0.

4. ## Re: Proving on Perfect Square?

The proof of this should be really simple if you recall what the formula for $\tau(n)$ is.