x^2 - ay^2 - bz^2 + abw^2 = 0
Source: IMO Shortlist 1989, Problem 25, ILL 83
September 18, 2008
number theoryDiophantine equationquadraticsequationIMO Shortlist
Problem Statement
Let which are not perfect squares. Prove that if x^2 \minus{} ay^2 \minus{} bz^2 \plus{} abw^2 \equal{} 0 has a nontrivial solution in integers, then so does x^2 \minus{} ay^2 \minus{} bz^2 \equal{} 0.