Combinatorial Number Theory

This group gathers theorems that answer counting and structural questions about integers using combinatorial reasoning, sitting between number theory proper and combinatorics. It covers results on binomial coefficients and their divisibility, such as Lucas' and Kummer's theorems, the Fibonacci-related identities of Zeckendorf, Carmichael, and Cassini and Catalan, and other combinatorial constructions, including Von Staudt-Clausen's theorem on Bernoulli numbers and the Erdos-Ginzburg-Ziv theorem on sequences forced to contain a multiple of a given length.