The Decomposition of 4(xp-1)/(x-1). II

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\u3c p\u3c 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\u3c 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

The Decomposition of 4(x^p-1)/(x-1)

If 4X = 4(xP-1)/(x-1) where p is an odd prime then 4X = Y2-(-1)(P-1)/2 pZ2, where Y and Z are polynomials in x with integral coefficients. For p = 37 we find the decomposition cited in Recherches sur la theorie des nombres by M. Kraitchik (1924) p. 126. For 37 ≤ p ≤ 61 the decomposition is given by Pocklington in Nature, VoL 107 (1921) pp. 456 and 587. For 67 ≤ p ≤ 97 the results are given by Gouwens in The Mathematical Monthly, Vol. 43, (1936) page 283. Herewith are presented the results for 101 ≤ p ≤ 199. For all decompositions Y is a polynomial of degree (p-1)/2 and Z is a polynomial of degree (p-3)/2. Y is listed first in each case, then Z

The groups of isomorphisms of groups of degree eight and of order less than forty-eight

Thesis (M.A.)--University of Illinois, 1911.Typescript.Includes bibliographical references (leaf 27)