Def: A polynomial f(x) with coefficients in Q (the rationals) is called a "numerical polynomial" if for all integers n, f(n) is an integer also.
I have to use induction to prove that for k > 0
that the function f(x) := (1/k!)*x*(x-1)...(x-k+1) is a numerical polynomial
I checked that this is true for k=1, but to be honest I'm not even sure what the dot dot dot means. If k=5 for say, I interpreted the dot dot dot as (1/5!)*x*(x-1)*(x-2)*(x-3)*(x-4). Is this the correct interpretation? If so it is indeed true for k=1, but nonetheless I don't know how to show that it is true for k+1.
Thanks so much.
P.S My professor sucks and it is really discouraging as a recently declared math major. So I will be on here often! Loves.