Localization (mathematics) | Mathematical principles | Diophantine equations | Algebraic number theory

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. (Wikipedia).

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Related pages

Prime ideal | Chinese remainder theorem | If and only if | Harold Davenport | Grunwald–Wang theorem | Local field | Hasse–Minkowski theorem | Helmut Hasse | Rational number | Matrix ring | Grothendieck–Katz p-curvature conjecture | Hardy–Littlewood circle method | Mathematics | Real number | E8 (mathematics) | Hermann Minkowski | Brauer group | Prime number | Diophantine equation | Quadratic form | Albert–Brauer–Hasse–Noether theorem | Birch's theorem | Christopher Hooley | P-adic number | Local analysis | Modular arithmetic | Central simple algebra