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The 40 pages that link to Prime factorization, each with the reason it gives.

• Prime numberRelated: Factoring RSA moduli would reveal the secret structure behind their keys.

• DivisibilityRelated: Comparing prime exponents gives a direct test for whether one positive integer divides another.

• FactorialRelated: Counting prime factors in n! reveals its divisibility and supports exact computation.

• Greatest common divisorRelated: Taking shared prime powers offers another way to compute a common divisor.

• Chinese remainder theoremRelated: Prime-power components reveal how the general theorem handles shared factors.

• Gödel numberingRelated: Gödel’s original scheme stores a sequence by using successive primes as exponents.

• Coprime integersRelated: Two integers are coprime precisely when their prime factorizations have no prime in common.

• Composite numberRelated: It breaks every composite number into its fundamental multiplicative factors.

• MultisetRelated: Prime factors form a multiset because a prime may appear repeatedly.

• Möbius functionRelated: Distinct prime factors determine the function's sign; repeated factors force zero.

• Sieve of EratosthenesRelated: Every composite below the limit is eliminated when one of its prime factors is processed.

• Bertrand's postulateRelated: Bounding prime powers in binomial coefficients exposes primes within the required interval.

• Least common multipleRelated: Taking the highest exponent of each prime across the inputs constructs their least common multiple.

• Perfect squareRelated: A positive integer is a square precisely when every prime has an even exponent in its factorization.

• Jacobi symbolRelated: The denominator’s prime factorization determines which Legendre symbols are multiplied.

• Euclid's theoremRelated: A prime factor of the constructed number supplies a prime absent from the proposed list.

• Fermat's theorem on sums of two squaresRelated: The generalized two-square criterion reads directly from the exponents in this factorization.

• Lowest termsRelated: Shared prime factors reveal exactly which factors can be canceled.

• Repeating decimalRelated: The denominator's prime factors determine whether a reduced fraction terminates in base ten.

• Divisibility ruleRelated: A divisibility shortcut may identify one required prime factor without finding a full factorization.

• Ramanujan–Nagell equationRelated: The power of two on the right makes divisibility and factorization central to the equation.

• Zsigmondy's theoremRelated: Zsigmondy's theorem guarantees a new prime factor as the exponent increases, with stated exceptions.

• Aliquot sequenceRelated: It provides an efficient route to the sum of all divisors.

• Beal's conjectureRelated: The conjecture asks whether the prime factorizations of all three bases overlap.

• Bruck–Ryser–Chowla theoremRelated: Prime exponents determine whether the required sum-of-two-squares representation is possible.

• Erdős–Graham problemRelated: Proof methods organize denominators by their prime factors to construct compatible unit fractions.

• Goldbach–Euler theoremRelated: It clarifies why Chen’s theorem permits a number with two prime factors.

• Grimm's conjectureRelated: The available choices for each composite come from its prime factorization.

• Lemoine's conjectureRelated: Unlike factorization, the conjecture asks for a representation built from a sum.