# Math Help - Gcd

1. ## Gcd

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)

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.