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a and b are both divisible by 11 when a^2+b^2 is divisible by 11

Source: 2020 Malaysia IMONST Round 2 Junior 3

September 22, 2021
number theorydivisibledivides

Problem Statement

Given integers aa and bb such that a2+b2a^2+b^2 is divisible by 1111. Prove that aa and bb are both divisible by 1111.
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