Find all positive integers a and b
Source: IMO Shortlist 1996, N4
August 9, 2008
floor functionnumber theoryequationalgebraIMO Shortlist
Problem Statement
Find all positive integers and for which
\left \lfloor \frac{a^2}{b} \right \rfloor \plus{} \left \lfloor \frac{b^2}{a} \right \rfloor \equal{} \left \lfloor \frac{a^2 \plus{} b^2}{ab} \right \rfloor \plus{} ab.