If n ≡ −1 (mod 24), then 24 divides

I have proven already that if is the prime factorization of n, then

.

Maybe that helps?

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- Mar 23rd 2010, 02:07 AMEinStonetwenty four and sum of divisors
**If n ≡ −1 (mod 24), then 24 divides**

I have proven already that if is the prime factorization of n, then

.

Maybe that helps? - Mar 23rd 2010, 10:45 AMchiph588@
Suppose .

Finding an inverse modulo is special because if it exists, .

Therefore .

Last but not least you need to show is not square. I'll let you take a stab at that. (Hint: Consider modulo .)

So we have then that - Mar 23rd 2010, 04:09 PMEinStone
Nice proof, just why is this fact true?

- Mar 23rd 2010, 05:09 PMchiph588@