Hello everbody...
Let b and c be relatively prime integers, and suppose a is an integer that is
divisible by both b and c. Prove that bc|a.
b and c divide a $\displaystyle \Rightarrow$ $\displaystyle a=hb=kc$ for some integers h and k.
b and c are relatively prime means there are integers $\displaystyle p,q$ such that $\displaystyle pb+qc=1$.
Now multiply through by a.
$\displaystyle pba+qca=a$ $\displaystyle \Rightarrow$ $\displaystyle a=pb(kc)+qc(hb)=(pk+qh)bc$.