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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
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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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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