anonymous
  • anonymous
Given a,b,n are positive integers. If a|n and b|n with gcd(a,b) = 1, prove ab|n
Mathematics
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anonymous
  • anonymous
Given a,b,n are positive integers. If a|n and b|n with gcd(a,b) = 1, prove ab|n
Mathematics
jamiebookeater
  • jamiebookeater
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ikram002p
  • ikram002p
a|n--->n=ak b|n--->n=bh Since gcd(a,b)=1 then there exist g =kh s.t n=abg thus ab|n
anonymous
  • anonymous
why does gcd(a,b) = 1 implies there is an integer g such that g = kh? @ikram002p
anonymous
  • anonymous
and why is n = abg?

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anonymous
  • anonymous
do u still need help
xapproachesinfinity
  • xapproachesinfinity
gcd(a,b)=1 then there is some integers l and s such that al+bs=1 so nal+nbs=n but then we know that a|n: n=ak b|n: n=bh bahl+abks=n from left we can deduce that ba divides it so must be true for the right too
anonymous
  • anonymous
@xapproachesinfinity Awesome! thank you! Didn't think gcd(a,b) = 1 = al+bs would be used in this case.
xapproachesinfinity
  • xapproachesinfinity
yeah! didn't understand what ikram did too i was trying to see through that for awhile
ikram002p
  • ikram002p
i guess i made mistake it not like g=kh xD that is wrong

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