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Integers as the sum of 3 integers.

  1. Jun 24, 2013 #1
    1. The problem statement, all variables and given/known data
    Prove that every integer >17 can be written as the sum of 3 integers >1 that are pairwise relatively prime.
    3. The attempt at a solution
    I already proved the case for even integers. Now im just working on the case for odd integers.
    I know that it has to be the sum of 3 odd integers because it cant be the sum of 2 even and one odd. I started with 2x+1=x+(x+1) where x is a positive integer. now either x or x+1 is even and I guess I could break the even one up as a sum of 2 odd numbers and then go from their.
     
  2. jcsd
  3. Jun 24, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    The proof (as an explicit construction of those 3 integers) for odd integers can be done similar to the proof for even integers, just with more casework.
     
  4. Jun 24, 2013 #3

    lurflurf

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    Homework Helper

    Did you finish the one about Prove that every integer >6 can be written as the sum of 2 integers >1 that are pairwise relatively prime? It is the same idea consider n/3-1,n/3,n/3+1 and adjust slightly in different cases.
     
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