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x^p + px^n + px^m +1 not a product of 2 integer polynomials

Source: 12th or 13th QEDMO problem 10 (11. - 15. 12. 2013) https://artofproblemsolving.com/community/c2400093_2013_qedmo_13th_or_12th

July 5, 2021
polynomialalgebraInteger Polynomial

Problem Statement

Let pp be a prime number gretater then 33. What is the number of pairs (m,n)(m, n) of integers with 0<m<n<p0 <m <n <p, for which the polynomial xp+pxn+pxm+1x^p + px^n + px^m +1 is not a product of two non-constant polynomials with integer coefficients can be written?
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