Prove that the product of any two integers of the form 6k + 1 is of that same form.

Solution

Let (6k + 1) be the first form and (6l + 1) be the second form

Product of both forms will be:

= (6k + 1)(6l + 1)

= 36kl + 6k + 6l + 1

= 6(6kl + k + l) + 1.

Thus, the product of two integers of the form 6n+1 is again of the form 6n + 1