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

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ISSN 1945-5844 (electronic)

ISSN 0030-8730 (print)

Vol. 99 (1982), No. 2, 379–386

DOI: 10.2140/pjm.1982.99.379

If p ≡ 1 (mod 2k) is a prime, the Jacobsthal sum Φ_k(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.

Primary: 10G15, 10G15

Received: 15 February 1980

Revised: 27 October 1980

Published: 1 April 1982