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Homework Help: Issue involving primes.

  1. Jan 1, 2015 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations
    I'm not sure what's relevant here.

    3. 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.
  2. jcsd
  3. Jan 1, 2015 #2


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    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?
  4. Jan 1, 2015 #3


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