If k is a positive integer and p is a prime with p ≡ 1 (mod 2k), then 2(p-1)/2k is a 2kth 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.

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Journal Pacific Journal of Mathematics
Citation
Hudson, R.H. (Richard H.), & Williams, K.S. (1983). Extensions of theorems of Cunningham-Aigner and Hasse-Evans. Pacific Journal of Mathematics, 104(1), 111–132.