Hasse principle

The Hasse principle, also known as the local-global principle, is a concept in number theory related to the solvability of equations over the rational numbers (or more generally, over a number field). It states that if a certain equation has solutions in local completions of the field (such as the p-adic numbers for various primes \( p \) and the real numbers), then it should also have a solution in the field itself.