This theorem is extended to the ring of polynomials by the Lagrangian interpolation problem.
This theorem is extended to the ring of polynomials by the Lagrangian interpolation problem. This theorem is used todiscover the secret in both the Mignotte and Asmuth-Bloom schemes for secret sharing. Kurt Godel proved his incompletenesstheorem by applying Cantor's pairing function and this theorem, which is also used by the Good-Thomas algorithm tore-index the data output in a fast Fourier transform. This theorem can be used to show that the number of reduced residueclasses for some integer m is equal to the Euler totient function applied to m. The RSA algorithm uses this theorem in the privatekey to accelerate decryption. An extension of this theorem shows an isomorphism between a quotient ring and a productof quotient rings. This theorem states that for the groups of integers n and a, where n are pairwise coprime integers, there isone integer congruent to a modulo n. For 10 points, name this important theorem from number theory, which was statedaround 1500 years ago by the mathematician Sunzi in the country for which it is named.
This theorem is extended to the ring of polynomials by the Lagrangian interpolation problem.
Chinese remainder theorem