Which numbers to choose?

Here, I found myself trying to choose a lot of numbers and testing each option.

I understood that choosing x as a multiple of 3 doesn’t make sense, so I chose other numbers.

But I want to be more smart about it.

Which numbers would you choose?

I think better than choosing numbers, maybe this is more easily solved by using/expanding on the property where the product of any 3 consecutive numbers would always be a multiple of 3.

Testing -1, 0, and 1 should capture all possible cases. This works because all integers can be expressed either as 3k -1, 3k, or 3k + 1