MathDB

Residues of a polynomial modulo p

Source: 2023 IMC #4

August 2, 2023

algebrapolynomialnumber theorymodular arithmeticprime numbersIMCIMC 2023

Problem Statement

Let

p

be a prime number and let

k

be a positive integer. Suppose that the numbers

a_i=i^k+i

for

i=0,1, \ldots,p-1

form a complete residue system modulo

p

. What is the set of possible remainders of

a_2

upon division by

p