Linked from

The 36 pages that link to Congruence relation, each with the reason it gives.

• Modular arithmeticRelated: It defines exactly when two integers count as the same value modulo a modulus.

• Equivalence relationBroader topic: Congruence relations preserve algebraic operations while grouping equivalent elements.

• Chinese remainder theoremNarrower topic: The theorem is stated entirely in terms of congruences.

• Fermat's little theoremNarrower topic: The theorem's conclusion is equality of residue classes modulo p.

• Group homomorphismRelated: A homomorphism's kernel induces a congruence identifying elements with the same output.

• Dirichlet's theorem on arithmetic progressionsRelated: A progression with difference q stays in one residue class modulo q.

• Quotient ringRelated: Congruence modulo an ideal expresses exactly which ring elements are identified.

• EqualityCompared with: Congruence can identify distinct integers modulo a number, unlike ordinary equality.

• Ideal (ring theory)Related: Congruence modulo an ideal supplies the equivalence relation behind quotient rings.

• Legendre symbolNarrower topic: The symbol tests whether congruence classes modulo p contain square roots.

• Quadratic residueRelated: It expresses the condition that an integer and a square represent the same residue.

• Modular exponentiationRelated: It gives the precise meaning of reducing a power modulo the modulus.

• Lagrange's four-square theoremRelated: Residue classes help rule out three-square representations and organize proof steps.

• Prime number theorem for arithmetic progressionsNarrower topic: The theorem groups primes according to congruence modulo q.

• Euler's criterionNarrower topic: The theorem compares a power and a Legendre-symbol value as residue classes.

• Presburger arithmeticRelated: Fixed-modulus congruences capture periodic properties expressible in the theory.

• RemainderRelated: Two integers have the same remainder exactly when they are congruent modulo the divisor.

• Symmetric relationBroader topic: Congruence is symmetric, so either object being congruent to the other gives the reverse relation.

• Equivalence classBroader topic: Compatibility lets equivalence classes inherit operations, as in quotient structures.

• Quotient setRelated: Unlike a bare equivalence relation, it supports quotient structures that inherit operations.

• Universal algebraRelated: Congruences make it possible to form quotient algebras while preserving operations.

• Algebraic structureRelated: Congruences are precisely the identifications that support quotient structures.

• Even numberRelated: Even integers form the residue class congruent to 0 modulo 2.

• Hilbert's axiomsRelated: Hilbert's congruence axioms govern equality of lengths and angles.

• Linnik's theoremRelated: It expresses the condition that a prime belongs to a specified residue class.

• Equality relationCompared with: Congruence can identify distinct elements while preserving structure; equality cannot.

• Solovay–Strassen primality testNarrower topic: The test's central comparison is an equality of residue classes modulo the candidate.

• Wilson's theoremNarrower topic: Wilson's theorem compares the factorial and −1 through congruence modulo n.

• Divisibility ruleRelated: Replacing powers of ten with congruent remainders makes many digit tests possible.

• Extended Euclidean algorithmRelated: Bézout coefficients translate gcd information into solvability of modular equations.

• Free objectRelated: Equations identify terms through a congruence when the category imposes identities.

• Rogers–Ramanujan identitiesRelated: Residue classes modulo five determine the allowed parts in the product formulations.

• PseudoprimeNarrower topic: Fermat-style pseudoprimality is defined by a congruence modulo the composite integer.

• Segment Addition PostulateRelated: Segment congruence supports substitutions among lengths in segment-addition arguments.

• Fundamental theorem on homomorphismsRelated: The homomorphism's equal-output relation respects the group operation.

• Goormaghtigh conjectureRelated: Reducing the equality modulo factors of either repunit yields arithmetic restrictions on the other base.