A quadratic partition of primes ≡1 (𝑚𝑜𝑑7)

Author:

Williams Kenneth S.

Abstract

The solutions of a quadratic partition of primes p 1 ( mod 7 ) p \equiv 1 \pmod 7 , in terms of which the author and P. A. Leonard have given the cyclotomic numbers of order seven and also necessary and sufficient conditions for 2, 3, 5 and 7 to be seventh powers ( mod p ) \pmod p , are obtained for all such primes > 1000 > 1000 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference7 articles.

1. On the septimic character of 2 and 3;Alderson, Helen Popova;Proc. Cambridge Philos. Soc.,1973

2. Cyclotomy and trinomial congruences;Dickson, L. E.;Trans. Amer. Math. Soc.,1935

3. E. KUMMER, "Sur les nombres complexes qui sont formés avec les nombres entiers réels et les racines de l’unité," J. Analyse Math., v. 12, 1847, pp. 185-212.

4. The septic character of 2, 3, 5 and 7;Leonard, Philip A.;Pacific J. Math.,1974

5. P. A. LEONARD & K. S. WILLIAMS, "A diophantine system of Dickson," Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (To appear.)

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