Vol. 99, No. 2, 1982

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Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums

Richard Howard Hudson and Kenneth S. Williams

Vol. 99 (1982), No. 2, 379–386
Abstract

If p 1 (mod 2k) is a prime, the Jacobsthal sum Φk(D) is defined by

        p∑−1 x(xk + D )
Φk(D ) =   (----p----) (k = 2,3,⋅⋅⋅ ).
x=1

It is shown how to evaluate Φ2(D) and Φ3(D) for any integer D.

Mathematical Subject Classification
Primary: 10G15, 10G15
Milestones
Received: 15 February 1980
Revised: 27 October 1980
Published: 1 April 1982
Authors
Richard Howard Hudson
Kenneth S. Williams