Problem #WSP-000378

Problem

Prove that each natural number $n \geq 2$ can be uniquely written as a product of prime factors. More precisely, there are prime numbers $p_{1}, \dots, p_{s}$ such that $n = p_{1} \dots p_{s}$ . Moreover, if $n = q_{1} \dots q_{l}$ where $q_{1}, \dots, q_{l}$ , then $s = l$ and after reordering we have $q_{1} = p_{1}, \dots, q_{s} = p_{s}$ . This is the fundamental theorem of arithmetic.

To see the solution register and get verified.