- #1

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## 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 = n

_{1}.n

_{2}; n

_{1}, n

_{2}not units. We may take n

_{1}, n

_{2}≥ 2. However we have n > n

_{1}, n > n

_{2}so n

_{1}, n

_{2}have prime factors.

I'm not sure how n > n

_{1}, n > n

_{2}implies that n

_{1}, n

_{2}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 > n

_{1}, n > n

_{2}implies that its true.