Fundamental Theorem of Arithmetic

Dependencies:

1. Euclid's lemma Used in proof
2. Every number has a prime factorization Used in proof

Proof

$n = p_1p_2\ldots = q_1q_2\ldots$

By Euclid's lemma, every $p_i$ must divide a $q_j$. We can prove this theorem using mathematical induction.

See complete proof on Wikipedia.

Dependency for:

1. Prime Factorization Exponent List (PFEL)

Info:

• Depth: 3
• Number of transitive dependencies: 4

Transitive dependencies:

1. Every number has a prime factorization
2. Integer Division Theorem
3. GCD is the smallest Linear Combination
4. Euclid's lemma