 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: Eric Roettger (University of Calgary)
Title: A Cubic Extension of the Lucas Functions
Time & Place: Friday, February 6, 4:00  5:00 pm, CL 313
Abstract
From 1876 to 1878 Lucas developed his theory of the functions Vn and
Un, which now bear his name. He was particularly interested in how these
functions could be employed in proving the primality of certain large inte
gers, and as part of his investigations succeeded in demonstrating that the
Mersenne number 2127
 1 is a prime. Vn and Un can be expressed in terms
of the nth
powers of the zeros of a quadratic polynomial, and throughout his
writings Lucas speculated about the possible extension of these functions to
those which could be expressed in terms of the nth
powers of the zeros of a
cubic polynomial. Indeed, at the end of his life he stated that "by searching
for the addition formulas of the numerical functions which originate from
