On the representation of integers by binary quadratic forms

Stanley Yao Xiao

Published 2017-04-01Version 1

In this note we show that for a given irreducible binary quadratic form $f(x,y)$ with integer coefficients, whenever we have $f(x,y) = f(u,v)$ for integers $x,y,u,v$, there exists a rational automorphism of $f$ which sends $(x,y)$ to $(u,v)$. This answers a question of D.~R.~Heath-Brown.