anonymous
  • anonymous
Number Thoery by Geogre Andrews page 68. Explain the part where it says "Let ni = M/mi. Since no two of the mi have a common factor, we see that gcd(ni, mi) = 1" Why?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
https://books.google.com/books?id=NV68AQAAQBAJ&lpg=PA58&pg=PA68#v=onepage&q&f=false
mathstudent55
  • mathstudent55
Wasn't that the supposition at the statement of the theorem above?
anonymous
  • anonymous
uhm.. no. The assumption was no two of the mi have a common factor. M = m1 * m2 * ...* ms ni = M / mi, the claim is gcd(ni,mi) = 1

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jim_thompson5910
  • jim_thompson5910
It has to do with how M is set up M = m1*m2*m3 ... *ms and how the mi's are pairwise coprime eg: If i = 2, then ni = M/mi n2 = M/m2 n2 = m1*m3*m4*...*ms n2 and m2 have no factors in common other than 1 because m2 and m1*m3*m4*...*ms have nothing in common other than 1
anonymous
  • anonymous
@jim_thompson5910 oh I see now. It has something to do with finding the greatest common factor of two numbers by prime factorization. (something I forgot I learned in grades school lol)
jim_thompson5910
  • jim_thompson5910
that is correct sometimes you'll see `gcd(a,b)` to mean `the greatest common factor of a and b` other times you may see `(a,b)` to mean the same thing
anonymous
  • anonymous
@jim_thompson5910 awesome. Thanks :)
jim_thompson5910
  • jim_thompson5910
you're welcome

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