Szabó, Sándor2024-09-042024-09-042005-12-01Teaching Mathematics and Computer Science, Vol. 3 No. 2 (2005) , 123-1291589-7389https://hdl.handle.net/2437/379553If two quadratic forms are equivalent, that is, if there is a linear transformation with integer coefficients and determinant 1 or −1 which takes one form to the other, then their ranges are the same and also their determinants are the same. The result of the paper is that for positive definite binary quadratic forms the converse is also true. Namely, if two positive definite binary quadratic forms of the same determinant have the same range, then they are equivalent. The arguments are guided by geometric considerations.application/pdfbinary quadratic formsequivalence of quadratic formsgeometry of numbersfolyóiratcikkOpen AccessSándor Szabóhttps://doi.org/10.5485/TMCS.2005.0069Teaching Mathematics and Computer Science23Teach. Math. Comp. Sci.2676-8364