The terms in the sequence 3, 7, 13, 21, …  are calculated by taking the product of two consecutive integers and adding 1, so that the n^th term is n(n+1) + 1.

Can you prove that none of the terms in the sequence will be a multiple of 5?

Are there any other integers that you can be sure will never divide exactly into any of the terms of the sequence? Remember to explain how you know.