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The 29 pages that link to Fundamental theorem of arithmetic, each with the reason it gives.

• Prime numberRelated: It makes primes the unique multiplicative building blocks of every integer.

• DivisibilityRelated: Its uniqueness makes divisibility reducible to comparing prime factors.

• Number theoryRelated: This theorem formalizes the role of primes as unique building blocks of positive integers.

• Prime factorizationRelated: It guarantees that prime factorization gives one definitive set of factors.

• Prime number theoremRelated: Prime factorization underlies the arithmetic identities used in proofs of prime distribution.

• Riemann zeta functionRelated: Unique prime factorization underlies the Euler product for ζ(s).

• Integer factorizationRelated: It guarantees that complete factorization has a unique answer.

• Goldbach's conjectureRelated: Goldbach concerns sums of primes, contrasting with the theorem's unique multiplicative decompositions.

• Disquisitiones ArithmeticaeRelated: The book treats unique prime factorization as a foundation for arithmetic investigations.

• Euclid's lemmaRelated: Euclid's lemma is the key step proving that two prime factorizations must match.

• Multiplicative functionRelated: Unique prime factorization lets prime-power values determine the function.

• Trial divisionRelated: This theorem guarantees that exhausting prime candidates yields the complete factorization.

• Sieve of EratosthenesRelated: Unique prime factors ensure every composite is reached by some prime’s multiples.

• Bézout's identityRelated: The prime-factor characterization of gcd complements its linear-combination characterization.

• Lagrange's four-square theoremRelated: Prime factorization extends prime representations to arbitrary positive integers.

• p-adic valuationRelated: Uniqueness ensures the exponent assigned to p is well-defined.

• Arithmetic functionRelated: Multiplicative functions are reconstructed from values at prime powers using unique factorization.

• Euclid's theoremRelated: The constructed integer must have a prime divisor, even if it is not itself prime.

• Catalan's conjectureRelated: Prime factorization is central to comparing hypothetical neighboring powers.

• Sophie Germain primeRelated: It underlies the factorization identities used to study expressions involving p.

• Bonse's inequalityRelated: It gives the product of primes its role as a canonical integer built from distinct prime factors.

• Grimm's conjectureRelated: Unique factorization makes each composite's set of prime divisors well-defined.