How do you prove if positive integers a,b,c that if gcd(a,b)=1 and a/bc then a/c (without use of Fund. Theorem of Arithmetic)

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Originally Posted by chadlyter How do you prove if positive integers a,b,c that if gcd(a,b)=1 and a/bc then a/c (without use of Fund. Theorem of Arithmetic) If gcd(a,b)=1 there exists x,y in Z such that, ax+by=1 (1) a|bc thus there exists k in Z such that bc=ak. (2) Multiply (1) by c to get, acx+bcy=c Substitute (2) to get, acx+aky=c a(cx+ky)=c Thus, a|c.

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