Extensions of theorems of Cunningham-Aigner and Hasse-Evans

Richard Howard Hudson and Kenneth S. Williams

Vol. 104 (1983), No. 1, 111–132

DOI: 10.2140/pjm.1983.104.111

Abstract

If k is a positive integer and p is a prime with p ≡ 1 (mod 2^k), then 2^(p−1)∕2k is a 2^k-th root of unity modulo p. We consider the problem of determining 2^(p−1)∕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