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I have the indefinite quadratic form $q(x,y,z) = 19 x^2 + 5 y^2 - z^2.$ It's not my fault. I find, on reflection, that I have no idea how to describe the orthogonal group of this over the integers. The thing is isotropic in $\mathbb Z,$ for example $19 + 45 = 64, $ and $76 + 5 = 81.$ Even if that were not the case, the orthogonal group would contain those for the binary forms $19 x^2 - z^2$ and $5 y^2 - z^2.$ Note that there is an answer for the original Pythagorean problem, Orthogonal group of quadratic form and to some extent http://en.wikipedia.org/wiki/Tree_of_Pythagorean_triples Oh, note that i found all null vectors of the form, https://math.stackexchange.com/questions/483496/pythagorean-triples-with-additional-parameters/483510#483510 which took two recipes because of an annoying odd even thing.

I have the indefinite quadratic form $q(x,y,z) = 19 x^2 + 5 y^2 - z^2.$ It's not my fault. I find, on reflection, that I have no idea how to describe the orthogonal group of this over the integers. The thing is isotropic in $\mathbb Z,$ for example $19 + 45 = 64, $ and $76 + 5 = 81.$ Even if that were not the case, the orthogonal group would contain those for the binary forms $19 x^2 - z^2$ and $5 y^2 - z^2.$ Note that there is an answer for the original Pythagorean problem, Orthogonal group of quadratic form and to some extent http://en.wikipedia.org/wiki/Tree_of_Pythagorean_triples Oh, note that i found all null vectors of the form, https://math.stackexchange.com/questions/483496/pythagorean-triples-with-additional-parameters/483510#483510 which took two recipes because of an annoying odd even thing.

I have the indefinite quadratic form $q(x,y,z) = 19 x^2 + 5 y^2 - z^2.$ It's not my fault. I find, on reflection, that I have no idea how to describe the orthogonal group of this over the integers. The thing is isotropic in $\mathbb Z,$ for example $19 + 45 = 64, $ and $76 + 5 = 81.$ Even if that were not the case, the orthogonal group would contain those for the binary forms $19 x^2 - z^2$ and $5 y^2 - z^2.$ Note that there is an answer for the original Pythagorean problem, Orthogonal group of quadratic form and to some extent http://en.wikipedia.org/wiki/Tree_of_Pythagorean_triples Oh, note that i found all null vectors of the form, http://math.stackexchange.com/questions/483496/pythagorean-triples-with-additional-parameters/483510#483510 which took two recipes because of an annoying odd even thing.

I have the indefinite quadratic form $q(x,y,z) = 19 x^2 + 5 y^2 - z^2.$ It's not my fault. I find, on reflection, that I have no idea how to describe the orthogonal group of this over the integers. The thing is isotropic in $\mathbb Z,$ for example $19 + 45 = 64, $ and $76 + 5 = 81.$ Even if that were not the case, the orthogonal group would contain those for the binary forms $19 x^2 - z^2$ and $5 y^2 - z^2.$ Note that there is an answer for the original Pythagorean problem, Orthogonal group of quadratic form and to some extent http://en.wikipedia.org/wiki/Tree_of_Pythagorean_triples Oh, note that i found all null vectors of the form, https://math.stackexchange.com/questions/483496/pythagorean-triples-with-additional-parameters/483510#483510 which took two recipes because of an annoying odd even thing.

I have the indefinite quadratic form $q(x,y,z) = 19 x^2 + 5 y^2 - z^2.$ It's not my fault. I find, on reflection, that I have no idea how to describe the orthogonal group of this over the integers. The thing is isotropic in $\mathbb Z,$ for example $19 + 45 = 64. $ Even if that were not the case, the orthogonal group would contain those for the binary forms $19 x^2 - z^2$ and $5 y^2 - z^2.$ Note that there is an answer for the original Pythagorean problem, Orthogonal group of quadratic form and to some extent http://en.wikipedia.org/wiki/Tree_of_Pythagorean_triples Oh, note that i found all null vectors of the form, http://math.stackexchange.com/questions/483496/pythagorean-triples-with-additional-parameters/483510#483510 which took two recipes because of an annoying odd even thing.

I have the indefinite quadratic form $q(x,y,z) = 19 x^2 + 5 y^2 - z^2.$ It's not my fault. I find, on reflection, that I have no idea how to describe the orthogonal group of this over the integers. The thing is isotropic in $\mathbb Z,$ for example $19 + 45 = 64, $ and $76 + 5 = 81.$ Even if that were not the case, the orthogonal group would contain those for the binary forms $19 x^2 - z^2$ and $5 y^2 - z^2.$ Note that there is an answer for the original Pythagorean problem, Orthogonal group of quadratic form and to some extent http://en.wikipedia.org/wiki/Tree_of_Pythagorean_triples Oh, note that i found all null vectors of the form, http://math.stackexchange.com/questions/483496/pythagorean-triples-with-additional-parameters/483510#483510 which took two recipes because of an annoying odd even thing.