Solution
= Solution
Use <strong induction> on the positive <integer> $n$. The case $n=1$ is represented by the <empty product>. For $n>1$, if $n$ is <prime> it is already a product of one <prime>. Otherwise $n=ab$ with $1<a,b<n$; the <induction hypothesis> gives <prime factorizations> for both $a$ and $b$, and concatenating them gives one for $n$. This proves existence in the <fundamental theorem of arithmetic> without presupposing uniqueness.