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The 62 pages that link to Modular arithmetic, each with the reason it gives.

• IntegerRelated: It studies integer calculations through their remainders.

• DivisibilityNarrower topic: It uses divisibility to define when two integers count as equivalent.

• Number theoryBroader topic: Congruences let number theorists study divisibility and periodic patterns through remainders.

• Diophantine equationRelated: Modular reductions provide quick necessary conditions for integer solutions.

• Greatest common divisorRelated: Coprimality with the modulus determines whether multiplication has an inverse.

• Chinese remainder theoremNarrower topic: It supplies the arithmetic setting in which the theorem operates.

• Fermat's little theoremRelated: It is the setting in which the theorem's power identity is expressed.

• Congruence (number theory)Narrower topic: Congruence is the relation that makes this arithmetic possible.

• Euler's totient functionNarrower topic: Coprime integers up to n represent the invertible residue classes modulo n.

• Fibonacci sequenceRelated: Fibonacci numbers modulo an integer form periodic patterns.

• Pierre de FermatRelated: Fermat’s little theorem became a foundational result in arithmetic modulo primes.

• Cyclic groupRelated: Residue classes modulo n form the additive cyclic group of order n.

• Quadratic reciprocityNarrower topic: The theorem compares square classes in two different modular systems.

• AdditionRelated: Addition can be performed on residue classes, with results reduced modulo a chosen integer.

• Primality testNarrower topic: Most efficient primality tests reduce huge powers to computations modulo the candidate integer.

• Quotient ringRelated: It is arithmetic inside the quotient ring of integers modulo a principal ideal.

• Ring (mathematics)Related: Residue classes form quotient rings that model modular calculations.

• Binary operationRelated: Remainder classes support binary operations that wrap around a finite set.

• Dirichlet L-functionRelated: Character values depend on residue classes modulo the character’s modulus.

• Euclid's lemmaRelated: Modulo the prime, a nonzero factor has a multiplicative inverse, forcing the other factor to vanish.

• Legendre symbolRelated: Its residue classes are the setting in which the symbol distinguishes squares from nonsquares.

• Quadratic residueNarrower topic: Quadratic residues are defined by equality of squares within this arithmetic.

• Modular exponentiationNarrower topic: Modular exponentiation is exponentiation performed within this arithmetic system.

• ArithmeticCompared with: It changes ordinary equality into congruence and makes calculations cyclic.

• Inverse elementRelated: Multiplicative inverses modulo an integer exist precisely for residues coprime to it.

• Parity bitRelated: Parity is the sum of bits modulo two.

• RemainderRelated: It treats equal remainders as the same arithmetic class.

• Shor's algorithmNarrower topic: The algorithm's order-finding subroutine studies powers and periods within modular arithmetic.

• SubtractionRelated: Subtraction still operates on residues, but results are interpreted modulo a fixed number.

• Perfect squareRelated: Squares occupy only certain remainder classes, ruling out many candidates.

• Two's complementNarrower topic: Fixed-width two's-complement addition behaves as arithmetic modulo the word size's power of two.

• Even numberNarrower topic: Calculating modulo 2 reduces parity questions to two residue classes.

• Finite cyclic groupRelated: Addition modulo the group order gives a standard model for every finite cyclic group.

• Jacobi symbolNarrower topic: Residues and congruences provide the setting for interpreting the symbol’s numerator.

• Multiplicative orderRelated: Residue classes provide standard examples of finite multiplicative groups.

• XOR gateRelated: Two-input XOR is addition modulo 2, but this arithmetic framing differs from gate behavior.

• Édouard LucasRelated: Congruences provide the language for expressing many of Lucas’s primality criteria.

• Fermat numberRelated: Congruences make Fermat numbers’ divisibility properties easier to express and prove.

• Hensel's lemmaNarrower topic: The initial root and its successive lifts are solutions in residue rings.

• Repeating decimalRelated: Repeated remainders in modular arithmetic account for cycles in decimal digits.

• Wilson's theoremNarrower topic: The theorem expresses factorials as congruences modulo n.

• Number (mathematics)Related: Modular arithmetic lets integers model cycles such as clock time and computer data.

• Sum of two squares theoremRelated: Residue classes modulo 4 divide primes into the cases used by the theorem.

• Caesar cipherRelated: The alphabet’s wraparound makes each letter shift an addition modulo 26.

• Collatz conjectureRelated: Congruence classes help describe possible sequences of odd and even steps.

• Divisibility ruleNarrower topic: Divisibility rules work by determining whether a number’s remainder modulo the divisor is zero.

• Erdős–Straus conjectureRelated: Residue classes organize proofs and computational checks of the conjecture.

• Star polygonRelated: Vertex selection advances by a fixed step modulo the polygon's number of vertices.

• PseudoprimeNarrower topic: Pseudoprime tests compare powers and residues within this arithmetic.

• Sophie Germain's identityRelated: The factors can be examined modulo primes to derive divisibility restrictions.