Easier to Follow Derivation of the Coefficients for p=2

  Here's an earlier version of the derivation of the coefficients for the partial sums of squares which is easier to follow than the general derivation. The subscript of the Σ indicates that the polynomial used is cubic and the number of layers for the partial sum is k. The polynomial is assumed to work for all values of k so it should work for k-1. The equations for the coefficients are obtained by equating the coefficients of corresponding powers of k. Then one can solve for the unknown coefficients one after another.

It's doubtful that the early Egyptians would have been able to do this. They did have complicated algorithms for solving math problems that are nearly algebraic in nature. The problem with assessing the capabilities of the Egyptians is that their methods may have been restricted to an elite and secluded like the inner sanctums of their temples. Pythagoras himself might have picked up his secretiveness from the Egyptian priests.