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different remainders am^3 + bm^2 + cm, mod 0,1,2,..., p-1

Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade, Round 4 p2

November 12, 2022
number theoryremainder

Problem Statement

Finding all quads of integers (a,b,c,p)(a, b, c, p) where p≥5p \ge 5 is prime number such that the remainders of the numbers am3+bm2+cmam^3 + bm^2 + cm, m=0,1,...,p−1m = 0, 1, . . . , p - 1, upon division of pp are two by two different..
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