Kaplansky's theorem on quadratic forms
theorem that a prime congruent to 1 modulo 16 is representable by either both or neither of the quadratic forms x²+32y² and x²+64y², while a prime congruent to 9 modulo 16 is representable by exactly one of the two
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Kaplansky's theorem on quadratic forms
Summary
Kaplansky's theorem on quadratic forms is a theorem[1]. It draws 3 Wikipedia views per month (theorem category, ranking #274 of 1,306).[2]
Key Facts
- Kaplansky's theorem on quadratic forms's instance of is recorded as theorem[3].
- Kaplansky's theorem on quadratic forms's part of is recorded as list of theorems[4].
- Kaplansky's theorem on quadratic forms's Freebase ID is recorded as /m/05b1dwb[5].
- Kaplansky's theorem on quadratic forms's proved by is recorded as Irving Kaplansky[6].
- Kaplansky's theorem on quadratic forms's defining formula is recorded as \begin{aligned}p\equiv1\pmod{16} &\implies \left(\left(\exists x,y\in\mathbb Z\colon p=x^2+32y^2\right)\iff \left(\exists x,y\in\mathbb Z\colon p=x^2+64y^2\right)\right) \p\equiv9\pmod{16} &\implies \left(\left(\exists x,y\in\mathbb Z\colon p=x^2+32y^2\right)\iff \left(\nexists x,y\in\mathbb Z\colon p=x^2+64y^2\right)\right) \end{aligned}[7].
- Kaplansky's theorem on quadratic forms's maintained by WikiProject is recorded as WikiProject Mathematics[8].
Why It Matters
Kaplansky's theorem on quadratic forms draws 3 Wikipedia views per month (theorem category, ranking #274 of 1,306).[2]