Hello All, I have an interesting problem I would like to propose to the number theory masterminds here. (For reference, this question came from the "For Thought" section of my text book, that is why it may seem a little odd)
Using a picture, we can describe a set of subsets within a square that resemble diagonals but aren't quite the same. We shall call these "steep diagonals". Notice one of them labelled 'd' in the square below, and there are 6 others parallel to it.
It can be proven under certain conditions that the sums of the positive (or negative) steep diagonals are constant providing that we are dealing with a square full of consecutive integers starting at 0.
My question to you all is: How can this be proven? What are the certain conditions that it is referencing?