(281) 1

Part of 1991 Tournament Of Towns

Problems(1)

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

Source:

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)

number theorySum of Squares