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Moldova TST, equation in positive integers

Source: Moldova TST 2014, First Day, Problem 1

March 4, 2014
quadraticsnumber theory proposednumber theory

Problem Statement

Find all pairs of non-negative integers (x,y)(x,y) such that x+y−x−y+2=0.\sqrt{x+y}-\sqrt{x}-\sqrt{y}+2=0.
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