MathDB
It almost never has solutions

Source: 2008 Greek TST,Pr.4

May 25, 2016
parameterizationnumber theory

Problem Statement

Given is the equation x2+y2−axy+2=0x^2+y^2-axy+2=0 where aa is a positive integral parameter.
i.i.Show that,for a≠4a\neq 4 there exist no pairs (x,y)(x,y) of positive integers satisfying the equation.
ii.ii. Show that,for a=4a=4 there exist infinite pairs (x,y)(x,y) of positive integers satisfying the equation,and determine those pairs.
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