Can anyone prove this?

 

If Tau(n) is an odd integer, then n is a perfect squre

 

Thanks,

Austin

Mabey I'm missing something, but is there any specific relationship between n and tau in this?

The tau I know of is the one such that tau(n) = the number of positive divisors of n.

From wolfram:

 

http://mathworld.wolfram.com/TauFunction.html

 

Although I have no idea as to how to solve the problem

Hmm, mathworld seems to define the tau slightly differently to the one I know. Though I think the original conjecture is true only for my definition of tau, something that mathworld calls sigma.

 

Either i'm missing something really basic, but it seems like a hard proof. I'll have a look through my algebra books.