AbstractLetf=f(x, y) be a quadratic form with real coefficients in two integer variablesx,y. LetV(f) be the set of values taken byf(x, y) at points (x, y) ≠ (0,0). Impose the same conditions on a second formf′. Trivially,fequivalent tof′ impliesV(f) =V(f′). It will be shown that the converse implication holds in general for definite forms; the obvious exceptionf=x2+xy+y2,f′=x2+ 3y2will be shown to be essentially the only one.