Quadratic diophatine equation
Source: Vietnam TST 2009, Problem 3
April 20, 2009
quadraticsDiophantine equationnumber theorynumber theory proposed
Problem Statement
Let a, b be positive integers. a, b and a.b are not perfect squares.
Prove that at most one of following equations
ax^2 \minus{} by^2 \equal{} 1 and ax^2 \minus{} by^2 \equal{} \minus{} 1
has solutions in positive integers.