I am reading Anderson and Feil - A First Course in Abstract Algebra.(adsbygoogle = window.adsbygoogle || []).push({});

I am currently focused on Ch. 8: Integral Domains and Fields ...

I need some help with an aspect of the proof of Theorem 8.6 ...

Theorem 8.6 and its proof read as follows:

In the above text, Anderson and Feil write the following:

" ... ... Conversely, if ##gcd(x,m) = d## and ##d \neq 1##, then ##m = rd## and ##x = sd##, where ##r## and ##s## are integers with ##m \gt r, s \gt 1##. ... ... "

I cannot see exactly why/how ##m \gt r, s \gt 1## ... can someone help me to prove that ##m \gt r## and ##s \gt 1## ... ... ?

Help will be appreciated ...

Peter

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# I Units in Z_m ... Anderson and Feil, Theorem 8.6 ... ...

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