If 4X = 4(xp - 1) / (x - 1) where p is an odd prime then 4X= Y2 - (- 1) p-1 / 2 pZ2, Y and Z being polynomials in x with integral coefficients. These decompositions for 100< p< 200 were given by the author in the Proceedings of the Iowa Academy of Science, 43: 255-262. This work has now been extended to values of p< 225. The decompositions are given herewith. For all decompositions Y is a polynomial of degree (p - 1) / 2 and Z a polynomial of degree (p- 3) / 2. The coefficients only are given in each case first for Y, then for Z.
Proceedings of the Iowa Academy of Science
© Copyright 1937 by the Iowa Academy of Science, Inc.
"The Decomposition of 4(xp-1)/(x-1). II,"
Proceedings of the Iowa Academy of Science, 44(1), 137-138.
Available at: https://scholarworks.uni.edu/pias/vol44/iss1/41