Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-17T05:49:41.659Z Has data issue: false hasContentIssue false
  • English
  • Français

On the congruence y2 ≡ x5 − a (mod p)

Published online by Cambridge University Press:  24 October 2008

A. R. Rajwade
A. R. Rajwade
Affiliation:
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh 14, India
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Rajwade, A. R.On rational primes p congruent to 1 (mod 3 or 5), Proc. Cambridge Philos.Soc. 66 (1969), 61–70.CrossRefGoogle Scholar
(2)Smith, H. J. S.Report on the theory of numbers (Chelsea).Google Scholar