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condition of sqrt(x)+sqrt(y)=sqrt(n) having solution

Source: Indonesia National Science Olympiad D2 P3

September 5, 2012
number theory proposednumber theory

Problem Statement

Let nn be a positive integer. Show that the equation x+y=n\sqrt{x}+\sqrt{y}=\sqrt{n} have solution of pairs of positive integers (x,y)(x,y) if and only if nn is divisible by some perfect square greater than 11.
Proposer: Nanang Susyanto
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