elementary number theory - Use mathematical induction to prove that any integer $nge2$ is either a prime or a product of primes.

Use strong mathematical induction to prove that any integer $n\ge2$ is either a prime or a product of primes.

I know the steps of weak mathematical induction...
Basis step: $p(n)$ for $n=1$ or any arbitrary $n_0$ ... show that it is true
Inductive hypothesis: $p(n)$ for $n=k$ ... Assume that it is true for $n=k$
Inductive step: $P(n)$ for $n=k+1$ ... Show that this is true for $n=k+1$

Answer

Strong induction means following: suppose $P(0)$ and that $P(k),k

For this question, our base is $n=2$, which is prime, so the statement holds. Now assume $n>2$ and that every $k