Re: Wanted: All Solutions of 3-Variable Polynomial

Dale Shoults wrote:

I would like all integer solutions of the following polynomial in three variables:

3^8 x^9 - 3^7 (a + b) x^6 + (3^5 (a + b)^2 - 2^3 3^3 a b) x^3 - (a + b)^3 = 0

if this is an easy question for someone.

All or none only please.



{(a,b,x) in Z^3: 6561x^9 - 2187(a + b) x^6 + (243(a + b)^2 - 216a b) x^3 - (a + b)^3 = 0}.

Sorry, I couldn't resist. Note that the set is infinite, since {(a, -a, 0): a in N}is a subset thereof.

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Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan

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