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Results tagged with binary-quadratic-forms
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user 287674
A binary quadratic form is a quadratic form in two variables.
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On the parity of the sum $\sum_{1\le j<k\le p-1\atop p\nmid aj^2+bjk+ck^2}(aj^2+bjk+ck^2)$
This is not a complete answer.
Claim 1. Let $D=b^2-4ac$. If $\left( \frac{D}{p}\right)=-1$, then $$S_p(a,b,c)\equiv a\frac{(p-1)^2}{4}+b\frac{(p-1)(p-3)}{8}\pmod{2}.$$
Proof.
Let $f(x,y)=ax^2+bxy+cy^ …
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