Let `f(x)=A x^2+B x+c ,w h e r eA ,B ,C` are real numbers. Prove that if `f(x)` is an integer whenever `x` is an integer, then the numbers `2A ,A+B ,a n dC` are all integer. Conversely, prove that if the number `2A ,A+B ,a n dC` are all integers, then `f(x)` is an integer whenever `x` is integer.