👉 Catalog math, also known as catalog theory or catalog arithmetic, is a branch of number theory that studies the properties and behavior of arithmetic functions defined on finite sets, particularly on the integers modulo a fixed prime or power of a prime. It involves analyzing functions like the sum of divisors, product of divisors, and Möbius functions, which count the number of divisors of integers with specific properties. A key concept is the "catalog," a collection of arithmetic functions indexed by a finite set, often the integers modulo \( n \). Catalog math explores how these functions interact and relate to each other, uncovering patterns and identities that reveal deep insights into the distribution of prime numbers and other number-theoretic phenomena. This area has applications in cryptography, coding theory, and computational number theory, as well as connections to other branches of mathematics like algebraic geometry and combinatorics.
