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\sqrt{x-\sqrt{y}}+ \sqrt{x+\sqrt{y}}= \sqrt{xy} diophantine

Source: Czech-Polish-Slovak Junior Match 2013, Individual p1 CPSJ

March 14, 2020

Diophantine equationdiophantinenumber theoryradical

Problem Statement

Determine all pairs

(x, y)

of integers for which satisfy the equality

\sqrt{x-\sqrt{y}}+ \sqrt{x+\sqrt{y}}= \sqrt{xy}