On the congruence y2 ≡ x5 − a (mod p)
Published online by Cambridge University Press: 24 October 2008
Extract
The object of this paper is to complete the half proved theorem 2 of (1).
Let be a primitive fifth root of unity. Any element of Z[ζ] is a polynomial f(ζ) in ζ of degree ≤ 3 since 1 + ζ + ζ2 + ζ3 + ζ4 = 0. The units of Z[ζ] are ± ζi(1 + ζ)i or better still , with 0 ≤ i ≤ 4, j ε Z, where is the fundamental unit of the maximal real subfield of Q(ζ).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 473 - 475
- Copyright
- Copyright © Cambridge Philosophical Society 1973
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