Given that each of p and q is a prime number:
Determine all possible pairs (p,q) that satisfy this equation:
p(p4+p2+10q) = q(q2+3)
(In reply to
re: Analytic solution with computer verification by Brian Smith)
You're right; I made a blunder.
My prior note was not a proof at all.
The truth is: RHS, q(q^2+3) is always positive
(p^4+p^2+10q) is always positive
So p can be even or odd.
I did the computer run first, and I think seeing that apparently p=2 was the only solution I was led down the primrose path and jumped to a conclusion (that parity would be the key to a proof). I barely looked at the LHS expression at all.
Will make a note in the earlier post.
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Posted by Larry
on 2024-02-18 09:23:00 |
re(2): Analytic solution with computer verification
