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Kosovo MO 2012 Grade 9, Problem 3

Source: Kosovo MO 2012 Grade 9, Problem 3

June 7, 2021

number theory

Problem Statement

The integers

a_1,a_2,...,a_{2012}

are given. Exactly

29

of them are divisible by

3

. Prove that the sum

a_1^2+a_2^2+...+a_{2012}^2

is divisible by

3

.

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