# Hasse Principle

### (Algebraic Number Theory)

Tech

###### Algebraic Number Theory ## What is Hasse principle?

In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the p-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers and in the p-adic numbers for each prime p.

### Technology Types

algebraic number theorydiophantine equationequationgeneralizationlocalization (mathematicsmathematical principlemathematical statementprinciplestatement

### Synonyms

Hasse principle for algebraic groupsLocal-global principleLocal–global principle

### Translations

Lokal-Global-Prinzip (Zahlentheorie) (de)Principe local-global (fr)Principe van Hasse (nl)哈瑟原則 (zh)局所大域原理 (ja)

## Tech Info

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— Date merged: 11/6/2021, 1:32:44 PM
— Date scraped: 5/20/2021, 5:55:32 PM