Interplay between the Chinese Remainder Theorem and the Lagrange Interpolation Formula

TL;DR

This paper presents a novel proof of the Lagrange Interpolation Formula using the Chinese Remainder Theorem applicable to arbitrary rings, offering a new perspective on their relationship.

Contribution

It introduces a new proof method connecting the Chinese Remainder Theorem with Lagrange Interpolation for general rings, expanding understanding beyond traditional contexts.

Findings

Proof of Lagrange Interpolation via Chinese Remainder Theorem for arbitrary rings

New perspective on the relationship between these two mathematical concepts

Potential applications in algebra and computational mathematics

Abstract

We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.