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Question:

We want to describe via a picture a set of subsets of a square which are something like diagonals, but are not quite the same. We'll call them steep diagonals. One of them, labelled e, is illustrated in the square below; the other 6 are parallel to it

x_e_x_x_x_x_x

x_x_x_x_e_x_x

e_x_x_x_x_x_x

x_x_x_e_x_x_x

x_x_x_x_x_x_e

x_x_e_x_x_x_x

x_x_x_x_x_e_x

State and prove a theorem about under what conditions we can expect that the sums on the positive ( or negative ) steep diagonals are constant, when we're dealing with a square full of consecutive integers starting at 0.

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# Homework Help: Can anyone guide me how to prove this question?

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