Kronecker symbol

generalization of the Jacobi symbol to all integers

Wikidata entity: Q1789847

P170	creator	...	Q76410 (Leopold Kronecker)	Leopold Kronecker
P2534	defining formula	Math	$\begin{aligned} (\frac{a}{u \prod_{i} p_{i}^{e_{i}}}) & = (\frac{a}{u}) \prod_{i} {(\frac{a}{p_{i}})}^{e_{i}} \\ (\frac{a}{0}) & = [a = \pm 1] \\ (\frac{a}{- 1}) & = {\begin{cases} 1 & a \geq 0 \\ - 1 & a < 0 \end{cases} \\ (\frac{a}{2}) & = {\begin{cases} 0 & 2 \| a \\ 1 & a \equiv \pm 1 (\mod 8) \\ - 1 & a \equiv \pm 3 (\mod 8) \end{cases} \\ (\frac{a}{p}) & \equiv a^{(p - 1) / 2} (\mod p) \end{aligned}$	???
P571	inception	...	1885-01-01	???
P31	instance of	...	Q11348 (function)	function
P31	instance of	...	Q24034552 (mathematical concept)	mathematical concept
P6104	maintained by WikiProject	...	Q8487137 (WikiProject Mathematics)	WikiProject Mathematics
P138	named after	...	Q76410 (Leopold Kronecker)	Leopold Kronecker
P2579	studied by	...	Q12479 (number theory)	number theory

External Ids

P646	Freebase ID	/m/034cx4
P2812	MathWorld ID	KroneckerSymbol
P12888	Metamath statement ID	df-lgs
P6366	Microsoft Academic ID (discontinued)	177217850

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