The author considers a random walk on the group of integers starting from the origin and whose steps admit as possible values exactly two integers $$a$$ and $$b$$ such that $$a < 0 < b$$. Then for the case $$a=-1$$ the author gives an explicit expression for the law of the first return time to the origin $P(T = n(b+1))={b \over n(b+1)-1} \binom{n(b+1)}{nb} p^{nb} (1-p) ^n,$ where $$p=P(X=-1)$$. The presentation is elegant and historical considerations are presented.