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On rational primes p congruent to 1 (mod 3 or 5)

Published online by Cambridge University Press:  24 October 2008

A. R. Rajwade
A. R. Rajwade
Affiliation:
Trinity College, Cambridge†
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Let p ≡ 1 (mod 3) or ≡ 1 (mod 5) be a rational prime and g a primitive root mod p. The non-zero residues g, g2,…,gp−1 (mod p) can then be divided into 3 or 5 classes , , , or , , , , respectively, by letting gν ∈ , , (respectively , , , , ) according as ν ≡ 0, 1, 2, (mod 3) (respectively 0, 1, 2, 3, 4 (mod 5)). Problems regarding the distribution of 1, 2, …, p − 1 amongst the 3 (respectively 5) classes are many. In this paper we consider the following problem in some detail (we shall state it here for the case p ≡ 1 (mod 3)). Let α, β, γ be typical members of , , respectively. Let the number of solutions of the congruences

be

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 1 , July 1969 , pp. 61 - 70
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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