Tag: Congruences

Normal Subgroups and Quotient Groups: The Condition for Multiplying CosetsFrom the wish to multiply cosets by their representatives we derive normality, prove that G/N is a group with a natural surjection onto it, and work out Z/nZ in full detail.MathematicsAlgebra: Groups, Rings and FieldsUndergraduateGroup theory Normal subgroups Quotient groups Cosets Congruences~32 min
Congruences and Fermat's Little Theorem: Computing in a World of RemaindersCongruence as an equivalence relation, the ring Z/nZ and its group of units, proofs of Fermat and Euler theorems, and the correctness of RSA via the Chinese remainder theorem.MathematicsNumber TheoryUndergraduateCongruences Modular arithmetic Fermat's little theorem Euler's totient RSA~6 min