Grunwald–Wang theorem
In algebraic number theory, the Grunwald–Wang theorem is a local-global principle stating that—except in some precisely defined cases—an element x in a number field K is an nth power in K if it is an nth power in the completion K p {\displaystyle K_{\mathfrak {p}}} for all but finitely many primes p {\displaystyle {\mathfrak {p}}} of K. For example, a rational number is a square of a rational number if it is a square of a p-adic number for almost all prime numbers p. It was introduced by Wilhelm Grunwald (1933), but there was a mistake in this original version that was found and corrected by Shianghao Wang (1948).