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1. Fundamental Theorem Of Arithmetic

   Linked via "strong induction"

   Existence
   The existence of a prime factorization is typically demonstrated by strong induction. Consider the smallest integer $n>1$ for which no prime factorization exists (the minimal counterexample).
   If $n$ is prime, the factorization is $n=n^1$, which is valid.
   If $n$ is composite, then $n = ab$ where $1 < a < n$ and $1 < b < n$. By the inductive hypothesis, both $a$ and $b$ …