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3a=x^2+2y^2 implies a=b^2+2c^2

Source: Serbia & Montenegro 2001 2nd Grade P1

June 2, 2021
number theory

Problem Statement

Let S={x2+2y2∣x,y∈Z}S=\{x^2+2y^2\mid x,y\in\mathbb Z\}. If aa is an integer with the property that 3a3a belongs to SS, prove that then aa belongs to SS as well.
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