📐 Fundamental Theorem of Arithmetic

Every integer greater than 1 can be expressed as a unique product of prime numbers (up to reordering).

Proof: **Existence:** We prove by strong induction. For $n = 2$, we're done (2 is prime). For $n > 2$, either $n$ is prime (done) or $n = ab$ for $1 < a, b < n$. By induction, both $a$ and $b$ have prime factorizations, so their product $n$ does too.

**Uniqueness:** Suppose $n = p_1 p_2 \\cdots p_k = q...

From: Cryptography Math

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