Quadratisches Reziprozitätsgesetz/53 mod 311/Lösung/Begründungslinks

Wir berechnen Schritt für Schritt das Legendre-Symbol.

	${}\left({\frac {53}{311}}\right)$	${}\,=\,$	${}\left({\frac {311}{53}}\right)$
	${}\,\,$	${}\,=\,$	${}\left({\frac {46}{53}}\right)$
	${}\,\,$	${}\,=\,$	${}\left({\frac {2}{53}}\right)\left({\frac {23}{53}}\right)$
	${}\,\,$	${}\,=\,$	${}-\left({\frac {23}{53}}\right)$
	${}\,\,$	${}\,=\,$	${}-\left({\frac {53}{23}}\right)$
	${}\,\,$	${}\,=\,$	${}-\left({\frac {7}{23}}\right)$
	${}\,\,$	${}\,=\,$	${}\left({\frac {23}{7}}\right)$
	${}\,\,$	${}\,=\,$	${}\left({\frac {2}{7}}\right)$
	${}\,\,$	${}\,=\,$	${}1$

Also ist ${}53$ ein Quadratrest modulo ${}311$.