Linked from

The 23 pages that link to Congruence (number theory), each with the reason it gives.

• DivisibilityRelated: Divisibility by a modulus is equivalent to congruence with zero.

• Diophantine equationRelated: Reducing an equation modulo an integer can expose impossible solution patterns.

• Quadratic reciprocityNarrower topic: Residues and squares in the theorem are defined through congruence.

• p-adic numberRelated: Agreement modulo p to high powers is the arithmetic form of p-adic closeness.

• Disquisitiones ArithmeticaeBroader topic: Gauss introduced the notation and systematic use of congruences that organize much of the book.

• Pell equationRelated: Congruence restrictions can rule out candidate solutions for particular values of D.

• p-adic valuationRelated: Valuation bounds translate directly into divisibility and congruence conditions modulo powers of p.

• Jacobi symbolRelated: The Jacobi symbol’s residue interpretation is expressed through congruences modulo its denominator.

• Fermat's theorem on sums of two squaresNarrower topic: The condition p ≡ 1 mod 4 selects exactly the odd primes covered by the representation.

• Vinogradov's theoremRelated: Local congruence restrictions determine whether a three-prime representation is arithmetically possible.

• Qin JiushaoNarrower topic: Congruences are the modular arithmetic statements combined in Qin’s method.

• Sum of two squares theoremNarrower topic: The condition distinguishes prime factors by their remainders modulo 4.

• Ramanujan–Nagell equationRelated: Congruences eliminate many possible values of x and n before deeper arguments are needed.

• Zsigmondy's theoremRelated: Prime divisors of aⁿ − bⁿ encode congruences between powers of a and b.

• Cubic reciprocityNarrower topic: Residue symbols encode whether congruences to cubes have solutions.

• Legendre's three-square theoremRelated: The forbidden family is described through powers of 4 and a residue class modulo 8.

• Lifting-the-exponent lemmaNarrower topic: LTE’s assumptions are commonly stated as congruences modulo a prime.

• Sophie Germain's theoremRelated: The proof tracks powers modulo p and 2p+1 to constrain possible solutions.

• Chevalley–Warning theoremRelated: Divisibility of the solution count is expressed as a congruence modulo the characteristic.

• Lucas's theoremNarrower topic: Its conclusion is a modular equality, not an equality of ordinary integers.

• Proth's theoremNarrower topic: The theorem expresses its test as a congruence to −1.

• Von Staudt–Clausen theoremRelated: The theorem is commonly expressed as a congruence modulo integers.

• Wolstenholme's theoremNarrower topic: The theorem states equality modulo the prime cube, not equality of ordinary integers.