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radical diophantine \sqrt{a+2\sqrt{b}}=\sqrt{a-2\sqrt{b}}+\sqrt{b}

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

January 20, 2020

number theoryradicalequationDiophantine equationdiophantine

Problem Statement

Find all pairs of positive integers

a, b

such that

\sqrt{a+2\sqrt{b}}=\sqrt{a-2\sqrt{b}}+\sqrt{b}