Base case so the proposition is true for the consecutive numbers .
Suppose the proposition is true for three consecutive numbers starting from .
Then divides , now consider the product of three consecutive integers starting for :
but divides and as one of and must be even divides , and so we conclude that divides .
Now we have proven the base case and that if the proposition is true for three consecutive integers starting from it is true for three consecutive integers starting from , and so by induction it is true for every set of
three consective positive integers.