If $0 \leq r \leq n$, is it possible to use this equation: $C( n, r ) = C( n - 1, r ) + C( n-1, r - 1 ).$ The problem is I want to prove that $C( n, r )$ is integers by induction. In other words, I have to prove $C( n + 1, r )$ is integer deducted from $C( n, r )$. I thought of the equation above but I found the condition for r is slightly different.
So is there any other equality that I can use for this problem?
Thanks,
Chan