Equations with a solution in the reals and in the p-adics for each prime p have a rational solution by the Hasse principle, an application of this statement. The decomposition of the finitely generated modules of a Dedekind domain into the direct sum of submodules is managed by this statement. The Good-Thomas algorithm for the fast Fourier transform uses this statement on the output, in conjunction with a mapping called Ruritanian on the input, to reindex data. An extension of this statement to principal ideal domains gives an isomorphism between a quotient ring and a product of quotient rings. For 10 points, name this statement that guarantees an integer solution to a set of congruence relations if the moduli are pairwise relatively prime.
Equations with a solution in the reals and in the p-adics for each prime p have a rational solution by the Hasse principle, an application of this statement. The decomposition of the finitely generated modules of a Dedekind domain into the direct sum of submodules is managed by this statement. The Good-Thomas algorithm for the fast Fourier transform uses this statement on the output, in conjunction with a mapping called Ruritanian on the input, to reindex data. An extension of this statement to principal ideal domains gives an isomorphism between a quotient ring and a product of quotient rings. For 10 points, name this statement that guarantees an integer solution to a set of congruence relations if the moduli are pairwise relatively prime.
Equations with a solution in the reals and in the p-adics for each prime p have a rational solution by the Hasse principle, an application of this statement.
Chinese remainder theorem