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## Homework Statement

Every positive integer n > 1 can be written as a product of primes.

Proof: We prove the result by strong induction on n, where n≥2.

Base Case: Note that 2 is prime, hence 2 = p

_{1}, where p

_{1}is prime.

Inductive Step: Let m ∈ ℤ with m ≥ 2 and assume for all integers k with 2 ≤ k ≤ m, k is a product of primes. We must prove that m + 1 is a product of primes.

We split into two cases, case 1 being m + 1 is prime, and case 2 being m + 1 is not prime.

Why do we use strong induction rather than induction?

## Homework Equations

## The Attempt at a Solution

I am a little bit confused are we using strong induction because it would not work if n is equal to 1?

If so, why else would we need to prove this with strong induction?