Consider a series of n independent repeated bernoulli

Question

Consider a series of n independent repeated Bernoulli trials at which the probability of success at each trial is p. Show that in order to have two successive integers, k₁ and k₂, between 0 and n, such that the probability of k₁ successes in the n trials will be equal to the probability of k₂ successes in the n trials, it is necessary and sufficient that (n + I)p be an integer