Suppose X is an integer- valued random variable. Show that in this case, X( 2n) = 1

Suppose X is an integer- valued random variable. Show that in this case, ϕX( 2πn) = 1 for any integer, n . Likewise, prove the reverse is also true. That is, show that if ϕX( 2πn) = 1 for any integer, n , the random variable X must be integer- valued.