find all primes of the form $\displaystyle n^4 - m^4 $

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- Jan 13th 2010, 08:19 AMflower3primes?
find all primes of the form $\displaystyle n^4 - m^4 $

- Jan 13th 2010, 08:29 AMDrexel28
- Jan 13th 2010, 08:41 AMDinkydoe
Maybe the question is: Show there don't exist primes of the form $\displaystyle n^4-m^4$?

- Jan 13th 2010, 08:41 AMDrexel28
- Jan 13th 2010, 08:46 AMDrexel28
There should be a subtle remark made here though. A prime is a natural number, so if $\displaystyle p=n^4-m^4$ we must have that $\displaystyle n^4>m^4\implies n>m$ so that we know that $\displaystyle n^2-m^2$ is a positive divisor.

- Jan 13th 2010, 09:16 AMDinkydoe
Aside from that: $\displaystyle (n^2-m^2) \neq 1$ for any n,m: n> m what would be required if p is prime.

- Jan 13th 2010, 09:19 AMDrexel28
- Jan 13th 2010, 10:48 AMMoo
I don't understand why you're debating oO

So the answer's just : there's none ! - Jan 13th 2010, 10:51 AMDrexel28
- Jan 13th 2010, 06:37 PMmr fantastic
I would prefer no more replies in this thread until the OP responds. Thankyou.