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a+b and a^2+b^2 are integers , then rational a,b are integers

Source: Czech-Polish-Slovak Match Junior 2019, team p1 CPSJ

January 20, 2020
number theoryrationalIntegers

Problem Statement

Rational numbers a,ba, b are such that a+ba+b and a2+b2a^2+b^2 are integers. Prove that a,ba, b are integers.
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