Auxiliary polynomial theorem
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The construction of auxiliary polynomials is an important concept in diophantine approximation and transcendental number theory.
[edit] Statement
Let β equal the cube root of b/a in the equation ax3 + bx3 = c and assume m is and integer that satisfies m + 1 > 2n/3 ≥ m ≥ 3 where n is a positive integer.
Then there exists
- F(X,Y) = P(X) + Y * Q(X)
such that
The auxiliary polynomial theorem states