Power Values of Certain Quadratic Polynomials

Details Power Values of Certain Quadratic Polynomials Power Values of Certain Quadratic Polynomials

2009-01-22

arxiv.org/abs/0901.3461v2

Mathematics

Number Theory

16 Pages; corrected and expanded version

Scientific paper

In this article we compute the $q$th power values of the quadratic polynomials $f$ with negative squarefree discriminant such that $q$ is coprime to the class number of the splitting field of $f$ over $\mathbb{Q}$. The theory of unique factorisation and that of primitive divisors of integer sequences is used to deduce a bound on the values of $q$ which is small enough to allow the remaining cases to be easily checked. The results are used to determine all perfect power terms of certain polynomially generated integer sequences, including the Sylvester sequence.

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