MathDB

25

Part of 1989 IMO Shortlist

Problems(1)

x^2 - ay^2 - bz^2 + abw^2 = 0

Source: IMO Shortlist 1989, Problem 25, ILL 83

9/18/2008
Let a,bāˆˆZ a, b \in \mathbb{Z} 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.
number theoryDiophantine equationquadraticsequationIMO Shortlist