If a|b and a|c, show that a|(bm+cn).
I have already proved that if x|y, and y|z, then x|z.
So, if a|b, then b|bm, so a|bm.
Also, if a|c, then c|cn, so a|cn.
So I think I need to show that a|aj+ai for some integers j=bm, i=cn.
ax = aj+ai
ax = a(j+i)
Let x = (j+i), thus ax = ax.
Could someone let me know if this proof is correct?