Congruences and Residues

Discrete Math · Axiom Academy

LESSON Congruences and Residues Understanding modular arithmetic: formal definitions, equivalent characterizations, arithmetic properties, and solving linear congruences. In other words, a and b have the same remainder when divided by n . This creates equivalence classes called residue classes or congruence classes . 2. Equivalent Characterizations The following statements are all equivalent ways to express : Congruence behaves nicely with addition, subtraction, and multiplication: The statement does NOT always imply . A linear congruence has the form . How do we solve for x ?

This is the written version of the interactive lesson above. See the full Discrete Math course.