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x^2 + y^2 - 5xy + 5 = 0

Source: Vietnam TST 1992 for the 33nd IMO, problem 5

June 25, 2005
quadraticsinvariantsymmetrynumber theory unsolvednumber theory

Problem Statement

Find all pair of positive integers (x,y)(x, y) satisfying the equation x2+y2−5⋅x⋅y+5=0.x^2 + y^2 - 5 \cdot x \cdot y + 5 = 0.
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