Linked from

The 61 pages that link to Divisibility, each with the reason it gives.

• Aliquot sequenceRelated: Every transition depends on which integers divide the current term.

• Lifting-the-exponent lemmaRelated: The lemma’s hypotheses specify which primes divide the bases and their differences or sums.

• Sophie Germain's theoremRelated: The proof forces divisibility conditions incompatible with a nonzero solution.

• Baranyai's theoremNarrower topic: The condition r divides n is necessary for each factor to cover all vertices.

• Greatest element and least elementRelated: Among positive divisors of a fixed integer, one is least and that integer is greatest.

• Grimm's conjectureRelated: A prime can be assigned to an integer only when it divides that integer.

• If and only ifRelated: Number-theoretic characterizations often state divisibility iff a remainder or factor condition holds.

• Join and meetRelated: For positive integers ordered by divisibility, join and meet are least common multiple and greatest common divisor.

• Midy's theoremRelated: The theorem’s sum is 10ⁿ − 1, a number divisible by 9 and composed of n nines.

• Proof that π is irrationalRelated: Divisibility constraints turn the constructed integral into an integer.

• Von Staudt–Clausen theoremRelated: The condition p−1 | 2n selects the primes in the denominator.