We have given that a∣bc and gcf(a,b)=1.
Thus there exist integers x,y such that
ax+by=1(1) and, as a∣bc , there exist integer k such that
ak=bc(2)
Now, multiply c in both side of the equation (1), we get
acx+bcy=c Now, using equation (2) we get
acx+aky=c⟹a(cx+ky)=c⟹a∣c
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