Consecutive numbers (or more properly, consecutive integers) are integers n_1 and n_2 such that n_2 - n_1 = 1, i.e., n_2 follows immediately after n_1. Given two consecutive numbers, one must be even and one must be odd. Since the product of an even number and an odd number is always even, the product of two consecutive numbers (and, in fact, of any number of consecutive numbers) is always even.

Catalan's conjecture | consecutive number sequences | even number | odd number