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TOT 281 1991 Spring O J1 sum of their squares is divisible by N

Source:

June 9, 2024

number theorySum of Squares

Problem Statement

N

integers are given. Prove that the sum of their squares is divisible by

N

if it is known that the difference between the product of any

N - 1

of them and the last one is divisible by

N

.
(D. Fomin, Leningrad)