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

Wikidata entity: Q17098379

P2534	defining formula	Math	$\begin{aligned} p \equiv 1 (\mod 16) & ⟹ ((\exists x, y \in ℤ : p = x^{2} + 32 y^{2}) ⟺ (\exists x, y \in ℤ : p = x^{2} + 64 y^{2})) \\ p \equiv 9 (\mod 16) & ⟹ ((\exists x, y \in ℤ : p = x^{2} + 32 y^{2}) ⟺ (∄ x, y \in ℤ : p = x^{2} + 64 y^{2})) \end{aligned}$	???
P31	instance of	...	Q65943 (theorem)	theorem
P6104	maintained by WikiProject	...	Q8487137 (WikiProject Mathematics)	WikiProject Mathematics
P361	part of	...	Q944443 (list of theorems)	list of theorems
P1318	proved by	...	Q129368 (Irving Kaplansky)	Irving Kaplansky

External Ids

P646

Freebase ID

/m/05b1dwb

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