MathDB

Divisibility problem

Source: Russian TST 2014, Day 8 P1 (Group NG), P2 (Groups A & B)

January 8, 2024

number theoryDivisibilityprime numbers

Problem Statement

Let

p{}

be a prime number and

x_1,x_2,\ldots,x_p

be integers for which

x_1^n+x_2^n+\cdots+x_p^n

is divisible by

p{}

for any positive integer

n{}

. Prove that

x_1-x_2

is divisible by

p{}.