SOLUTION: here is my query... Let a(x); b(x) and c(x) be polynomials with complex coeffcients such that gcd(a(x); b(x); c(x)) = 1 (i.e. no polynomial of degree >= 1 divides all the th

Question 550956: here is my query...
Let a(x); b(x) and c(x) be polynomials with complex coeffcients such that
gcd(a(x); b(x); c(x)) = 1
(i.e. no polynomial of degree >= 1 divides all the three) and deg(a).deg(b).deg(c) =0
0. Prove that,
a(x)
^n + b(x)
^n != c(x)
^n
for all n >= 3

(!= => "not equal to")
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Unless I'm mis-interpreting your question, if deg(a)*deg(b)*deg(c) = 0, then one of the polynomials must be a constant.

If alpha, beta, gamma are the constant terms of each polynomial, then by equating constant terms on both sides, we have

However, alpha, beta, gamma have to be positive integers for Fermat's Last Theorem to apply. Your polynomials have complex coefficients, so you'll be in for a long run...
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SOLUTION: here is my query... Let a(x); b(x) and c(x) be polynomials with complex coeffcients such that gcd(a(x); b(x); c(x)) = 1 (i.e. no polynomial of degree >= 1 divides all the th

SOLUTION: here is my query... Let a(x); b(x) and c(x) be polynomials with complex coeffcients such that gcd(a(x); b(x); c(x)) = 1 (i.e. no polynomial of degree >= 1 divides all the th