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On Euler’s criterion
for quintic nonresidues
Kenneth S. Williams |
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Vol. 61 (1975), No. 2, 543–550
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Abstract |
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Let p be a prime ≡ 1 (mod 5). If 2 is a quintic nonresidue (mod p) then 2p−1∕5 ≡ α (mod p) for some fifth root of unity α5(≢1) (mod p). Emma Lehmer has given an explicit expression for α5 in terms of a particular solution of a certain quadratic partition of p. In this paper we show how in principle the corresponding result can be obtained for any quintic nonresidue D (mod p). Full details are given for D = 2,3,5. |
Mathematical Subject Classification
Primary: 10A10, 10A10
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Milestones
Received: 4 June 1974
Revised: 8 August 1975
Published: 1 December 1975
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Authors |
| Kenneth S. Williams | |
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