Track / Stage 4 / 170 of 340 #430 of 2000

17. Find integers $a, b, c$ such that $0<|c|<|b|<|a|$, and make $x(x-a)(x-b)(x-c)+1$ irreducible with integer coefficients.

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Official solution

17. The original expression is irreducible if and only if $(a, b, c) \neq(1,2,3)$ and $(-1,-2,-3)$.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.