Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 1G / a / Solution

Write $f=[a,b,c]$. Two integral binary quadratic forms $f$ and $g$ are equivalent if there is a matrixsuch thatEquivalently, the group ${\mathrm{SL}}_2(\mathbb{Z})$ acts on forms by integral unimodular changes of variables.