Number theory problem

  • Thread starter yeland404
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  • #1
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Homework Statement



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

Homework 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


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
 

Answers and Replies

  • #2
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(a,b)=1, thus consider the prime factorization of e.
 
  • #3
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There exists integers x, y such that ax+by=1. Therefore c=acx+bcy=abrx+basy.
 

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