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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It has to do with how M is set up
M = m1*m2*m3 ... *ms
and how the mi's are pairwise coprime
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
@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)
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