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Nov
29
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Jul
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Jul
14
comment Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers)
I don't think Dr. Weissmann has gotten to Conway's topograph yet in his blog. If he's written about it somewhere, I'd love to read it. My understanding is that he is the authority in the topograph method and its generalizations.
Jul
13
comment Solve $37x^2-113y^2=n$
@Hecke One of my favorite quotes: "To improve upon Hecke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task." --- André Weil
Jul
13
comment Solve $37x^2-113y^2=n$
@Hecke There was a gap in my proof because I did not take into account the fact that $16724$ is not a fundamental discriminant. I think I fixed it. By the way, does your nickname have anything to do with Erich Hecke?
Jul
13
revised Solve $37x^2-113y^2=n$
Fixed gap in proof from not considering fundamental discriminant. Rearranged material, added section on further comments.
Jul
13
awarded  Yearling
Jul
13
answered Solve $37x^2-113y^2=n$
Jun
15
comment Matrix of quadratic form has to be symmetric?
The section you linked to is about forms over $\mathbb{R}$, which has characteristic not equal to 2. Over such fields, we do not get any new quadratic form by considering non-symmetric matrices because we can divide by 2. So $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ gives the same quadratic form as $\begin{pmatrix} a & \frac{b+c}{2} \\ \frac{b+c}{2} & d \end{pmatrix}$.
Jun
7
revised Diagonalising quadratic form
added 388 characters in body
Jun
7
answered Diagonalising quadratic form
May
27
answered How to find $A$ such that $A^2$ is the zero matrix?
Mar
28
awarded  Editor
Mar
28
revised Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers)
Provide a better example of the versatility of Conway's topograph
Mar
28
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Mar
28
answered Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers)
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24
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