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

Question

ikram002p · Answer

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 · Answer

why does gcd(a,b) = 1 implies there is an integer g such that g = kh? @ikram002p

anonymous · Answer

and why is n = abg?

anonymous · Answer

do u still need help

xapproachesinfinity · Answer

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 · Answer

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

xapproachesinfinity · Answer

yeah!
didn't understand what ikram did too
i was trying to see through that for awhile

ikram002p · Answer

i guess i made mistake it not like g=kh xD that is wrong