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Homework Help: Number theory problem

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data

    a,b,c belong to Z with (a,b)=1. Prove that if a|c and b|c, then ab|c

    2. Relevant equations
    let a1,a2.....an, c belong to Zwith a1....an pairwise relatively prime, prove if ai|c for each i, then a1a2....an|c


    3. The attempt at a solution

    if a|c, then c=ea, b|c, then c=fb, then which the next step and how it relates with (a,b)=1
     
  2. jcsd
  3. Jan 15, 2012 #2
    (a,b)=1, thus consider the prime factorization of e.
     
  4. Jan 16, 2012 #3
    There exists integers x, y such that ax+by=1. Therefore c=acx+bcy=abrx+basy.
     
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