Diophantus of Alexandria

  There's an easier way still to find the coefficients of the formula for Pythagoras' partial sums of integers. One just sets up a set of linear equations by substituting values of n and the partial sum, Σ. The same can be done for series involving higher powers but more equations would be needed to determine the coefficients.

Diophantus certainly could have done this. He was able to solve 6th degree polynomials. His notation for a polynomial was similar to that used for weights and measures. One might contain a multiple of a cube of an unknown plus another multiple of squares of the unknown plus a multiple of the unknown plus a number of units. The Greek alphabet was used to represent numbers so ɑ=1, ιγ=13, ε =5 and β=2 in the example cited. The title of Diophantus' Book was Arithmetica which comes from the Greek work for number, αριθμός, which of course Diophantus used.