10

Part of 2013 QEDMO 13th or 12th

Problems(1)

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

p

be a prime number gretater then

3

. What is the number of pairs

(m, n)

of integers with

0 <m <n <p

, for which the polynomial

x^p + px^n + px^m +1

is not a product of two non-constant polynomials with integer coefficients can be written?

polynomialalgebraInteger Polynomial