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Nice polynomial

Source: Romanian TST 1 2006, Problem 2

April 19, 2006
algebrapolynomialalgebra proposed

Problem Statement

Let pp a prime number, p≥5p\geq 5. Find the number of polynomials of the form x^p + px^k + p x^l + 1,   k > l,   k, l \in \left\{1,2,\dots,p-1\right\}, which are irreducible in Z[X]\mathbb{Z}[X].
Valentin Vornicu
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