Vol. 104, No. 1, 1983

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Extensions of theorems of Cunningham-Aigner and Hasse-Evans

Richard Howard Hudson and Kenneth S. Williams

Vol. 104 (1983), No. 1, 111–132
Abstract

If k is a positive integer and p is a prime with p 1 (mod 2k), then 2(p1)2k is a 2k-th root of unity modulo p. We consider the problem of determining 2(p1)2k modulo p. This has been done for k = 1,2,3 and the present paper treats k = 4 and 5, extending the work of Cunningham, Aigner, Hasse, and Evans.

Mathematical Subject Classification
Primary: 10A15, 10A15
Secondary: 10G15
Milestones
Received: 19 November 1979
Revised: 18 August 1981
Published: 1 January 1983
Authors
Richard Howard Hudson
Kenneth S. Williams