MathDB

4

Part of 2008 Greece Team Selection Test

Problems(1)

It almost never has solutions

Source: 2008 Greek TST,Pr.4

5/25/2016
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.
parameterizationnumber theory