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anonymous

  • one year ago

Given a,b,n are positive integers. If a|n and b|n with gcd(a,b) = 1, prove ab|n

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  1. ikram002p
    • one year ago
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    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

  2. anonymous
    • one year ago
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    why does gcd(a,b) = 1 implies there is an integer g such that g = kh? @ikram002p

  3. anonymous
    • one year ago
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    and why is n = abg?

  4. anonymous
    • one year ago
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    do u still need help

  5. xapproachesinfinity
    • one year ago
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    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

  6. anonymous
    • one year ago
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    @xapproachesinfinity Awesome! thank you! Didn't think gcd(a,b) = 1 = al+bs would be used in this case.

  7. xapproachesinfinity
    • one year ago
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    yeah! didn't understand what ikram did too i was trying to see through that for awhile

  8. ikram002p
    • one year ago
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    i guess i made mistake it not like g=kh xD that is wrong

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