arithmeticae

r infinitude. Studies the behavior of primes in different residue classes. Explores the distribution of primes and establishes preliminary results towards the prime number theorem. Book III: Quadratic Residues and Reciprocity Develops the theory of quadratic residue

eave the same remainder when divided by \(m\). Gauss’s systematic treatment of congruences allowed mathematicians to solve complex equations in modular systems, analyze periodicity, and explore the properties of prime numbers more deeply. Quadratic Recip