An Algebraical Identity

Abstract

WITH reference to the letters in NATURE of June 9 and July 7 by Dr. G. B. Mathews, Dr. H. C. Pocklington, and the Rev. J. Cullen on the polynomials Y(x), Z(x) satisfying the identity may I point out that Y(x)²,- 2(-)^(p-1) Z(x)² = 4(x)²(x-1)are tabulated as far as p=101 in Dr. Hermann Teege' inaugural dissertation, “Ueber die ½(p−1) gliedrigen Gaussischen Perioden” (Kiel, Peters, 1900)? Connected with these polynomials there is a further point which, so far as I am aware, has not yet been settled. When x=1 and p1 (mod. 4), Y(x)=py, Z(x)=z, and py²z²=4.