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9|(x+a)(x+b)(x+c)-x^3-1 doesn't hold for some x and all a,b,c

Source: Bulgaria 1972 P1

June 21, 2021
number theory

Problem Statement

Prove that there are don't exist integers a,b,ca,b,c such that for every integer xx the number A=(x+a)(x+b)(x+c)−x3−1A=(x+a)(x+b)(x+c)-x^3-1 is divisible by 99.
I. Tonov
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