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A class of irreducible polynomials

Joshua HarringtonLenny Jones — 2013

Colloquium Mathematicae

Let f ( x ) = x + k n - 1 x n - 1 + k n - 2 x n - 2 + + k x + k [ x ] , where 3 k n - 1 k n - 2 k k 2 k n - 1 - 3 . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of 2 k n - 1 - 3 on the coefficients of f(x) is the best possible in this situation.

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