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From: num-curious on 11 Mar 2010 17:12
Thanks again for all the replies.

Modified conditions a bit more:

1. p, q, r are distinct integers (assume all > 0).
2. n is an odd prime
3. (p) > (q+r)
4. q = a^n; r = b^n (a, b are integers)
5. (npqr)(2^n) divides (p-q-r)^n

Is (5) possible when p, q, r are relatively prime? If not, can it be proved that it is not possible using multinomial theorem or any elementary algebra?

Thanks!
From: Gerry Myerson on 15 Mar 2010 00:30
In article
<1643769594.367296.1268381584945.JavaMail.root(a)gallium.mathforum.org>,
num-curious <govegannow(a)gmail.com> wrote:

> Thanks again for all the replies.
>
> Modified conditions a bit more:
>
> 1. p, q, r are distinct integers (assume all > 0).
> 2. n is an odd prime
> 3. (p) > (q+r)
> 4. q = a^n; r = b^n (a, b are integers)
> 5. (npqr)(2^n) divides (p-q-r)^n
>
> Is (5) possible when p, q, r are relatively prime? If not, can it be proved
> that it is not possible using multinomial theorem or any elementary algebra?

Are you, by any chance, trying to prove Fermat's Last Theorem
by highschool algebra?

--
Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
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