This group gathers theorems built on the arithmetic of remainders, the study of numbers that agree modulo some fixed base. It covers the elementary machinery of the subject, including the division algorithm, the Chinese remainder theorem, and Bezout's identity, together with the family of small-prime congruence theorems associated with Fermat, Euler, and Wilson, and later refinements such as Wolstenholme's and Midy's theorems that uncover further hidden regularities in how numbers behave under a fixed modulus.
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Era Of Emergence All Congruences and Modular Arithmetic
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1. Modular Arithmetic (Wikipedia)
Wikimedia FoundationIntroduction sectionQuote, Introduction section
The modern approach to number theory using modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.
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