Are n1 and n2 Prime Factors of n?

[Calu]

Homework Statement

We have n ≥ 2, n not prime, n ∈ ℤ. Take the smallest such n. n is not prime and as such n is not irreducible and can be written as n = n₁.n₂; n₁, n₂ not units. We may take n₁, n₂ ≥ 2. However we have n > n₁, n > n₂ so n₁, n₂ have prime factors.

I'm not sure how n > n₁, n > n₂ implies that n₁, n₂ have prime factors.

Homework Equations

I'm not sure what's relevant here.

The Attempt at a Solution

From what I can see, the lowest possible n which meets the criteria is 6. 6 has the prime factors 2 and 3, which means that obviously what is stated is true. I'm just not sure how n > n₁, n > n₂ implies that its true.

 

[Orodruin]

6 is not the smallest non-prime integer larger than or equal to 2, 4 is.

Anyway, if n is the smallest non-prime integer and n1 < n, what does this imply?

 

[haruspex]

Do you mean, "n₁, n₂ are prime factors"?