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Sum of two squares

Source: Baltic Way 2017 Problem 20

November 11, 2017
number theory

Problem Statement

Let SS be the set of all ordered pairs (a,b)(a,b) of integers with 0<2a<2b<20170<2a<2b<2017 such that a2+b2a^2+b^2 is a multiple of 20172017. Prove that ∑(a,b)∈Sa=12∑(a,b)∈Sb.\sum_{(a,b)\in S}a=\frac{1}{2}\sum_{(a,b)\in S}b.
Proposed by Uwe Leck, Germany
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