The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms
Peters, Meinhard
Experiment. Math., Tome 13 (2004) no. 1, p. 273-274 / Harvested from Project Euclid
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There are 18 (and possibly 19) integers that are not of the form $ xy + yz + xz $ with positive integers $x, y, z$. The same 18 integers appear as exceptional discriminants for which no indecomposable positive definite binary quadratic form exists. We show that the two problems are equivalent.
Publié le : 2004-05-14
Classification:  Binary quadratic forms,  Diophantine equations,  11E12,  11E96,  11D09 
@article{1103749835,
     author = {Peters, Meinhard},
     title = {The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms},
     journal = {Experiment. Math.},
     volume = {13},
     number = {1},
     year = {2004},
     pages = { 273-274},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1103749835}
}

Peters, Meinhard. The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms. Experiment. Math., Tome 13 (2004) no. 1, pp.  273-274. http://gdmltest.u-ga.fr/item/1103749835/