KnowraCongruence relationLinked fromLinked fromThe 36 pages that link to Congruence relation, each with the reason it gives.All 36Broader topic 3Related 23Narrower topic 8Compared with 2Modular arithmeticRelated: It defines exactly when two integers count as the same value modulo a modulus.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.Ideal (ring theory)Related: Congruence modulo an ideal supplies the equivalence relation behind quotient rings.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.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.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.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.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.
KnowraCongruence relationLinked fromLinked fromThe 36 pages that link to Congruence relation, each with the reason it gives.All 36Broader topic 3Related 23Narrower topic 8Compared with 2Modular arithmeticRelated: It defines exactly when two integers count as the same value modulo a modulus.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.Ideal (ring theory)Related: Congruence modulo an ideal supplies the equivalence relation behind quotient rings.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.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.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.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.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.