Linked from

The 12 pages that link to Euclid's lemma, each with the reason it gives.

• Prime numberRelated: This divisibility rule underlies uniqueness of prime factorization.

• DivisibilityRelated: It explains why prime factors control divisibility of products.

• Fundamental theorem of arithmeticRelated: This divisibility rule forces any prime in one factorization to appear in every other.

• Irrational numberRelated: It helps prove that square roots of primes cannot be ratios of integers.

• Unique factorization domainRelated: It lets prime factors be matched across two factorizations.

• Sieve of EratosthenesRelated: The lemma underlies the guarantee that composites have a prime divisor among the sieve’s candidates.

• Rational root theoremRelated: Prime-factor reasoning establishes the theorem’s numerator and denominator divisibility conditions.

• Unique factorizationRelated: Canceling a shared prime factor relies on this divisibility result.

• Euclid's theoremRelated: It clarifies why no listed prime divides one plus their product.

• Wilson's theoremRelated: The composite case uses prime divisors to rule out the required factorial congruence.

• Euclid–Euler theoremRelated: The converse proof uses prime divisibility to constrain the odd factor of an even perfect number.

• Extended Euclidean algorithmRelated: It is a foundational result about divisibility and coprimality surrounding gcd computations.