# Proving on Perfect Square?

• Aug 20th 2012, 07:41 PM
musngiburger
Proving 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 PM
richard1234
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.
• Aug 20th 2012, 08:59 PM
musngiburger
Re: 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 PM
Vlasev
Re: Proving on Perfect Square?
The proof of this should be really simple if you recall what the formula for $\tau(n)$ is.