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anonymous
 one year ago
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?
anonymous
 one year ago
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?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0https://books.google.com/books?id=NV68AQAAQBAJ&lpg=PA58&pg=PA68#v=onepage&q&f=false

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Wasn't that the supposition at the statement of the theorem above?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0uhm.. 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3It 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
 one year ago
Best ResponseYou've already chosen the best response.0@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
 one year ago
Best ResponseYou've already chosen the best response.3that 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
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 awesome. Thanks :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3you're welcome
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