## Franklin's Notes

### Integrally equivalent forms

Two forms $F,G$ of the same degree (sometimes with rational coefficients) are called integrally equivalent if there exists a linear change of variables with rational integer coefficients taking one to the other, and vice versa. For instance, the forms are integrally equivalent, as evidenced by the change of variables $x\mapsto u+v$ taking $F$ to $G$, or the change of variables $u\mapsto x, v\mapsto 0$ taking $G$ to $F$.