Let P be the product of three consecutive integers. What is the greatest integer that always divides P?
I personally don't think that this question makes much sense. If you think about it - there are infinite consecutive integers, therefore, there are infinite integers that divide by P. Are there any numbers in this question that I am not aware of? If so, please add them (it'll help a lot). Thanks!
I believe the answer is 6. After testing out a few cases, it becomes obvious that there is always a multiple of 2 and a multiple of 3 in three consecutive integers.
I'm don't know a rigorous way to prove it though.