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The book just states that ab|c if (a,b)=1...so I took a stab on proving it:

(a,b)=1 means au+bv=1

so for no reason at all I threw in a c

acu+bcv=c

since a|c and b|c c=ak and c= bh

abhu+bakv=c

this means ab(hu+kv)=c

hence ab|c

It this proof right...the book kind of skips proving this proposition.