As a Ninth Power (Mod p)

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Authors

  • Kenneth S. Williams
     Carleton University, Ottawa, Ontario ,CA

Abstract

Let p be a prime ≠ 2,3. We consider the problem of giving a necessary and sufficient condition for 2 to be a ninth power (mod p), analogous to those known for 2 to be a k th power (mod p) for k = 3 [3], k = 5 [4], k = 7 [5] and k = 11 [6].

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Published

1975-12-01

How to Cite

Williams, K. S. (1975). As a Ninth Power (Mod p). The Journal of the Indian Mathematical Society, 39(1-4), 167–172. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16644

Issue

Volume 39, Issue 1-4, March-December 1975

Section

Articles

License

Copyright (c) 1975 Kenneth S. Williams

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

L.D. BAUMERT AND H. FREDRICKSEN, The cyclotomic numbers of order eighteen with applications to difference sets. Math. Comp. 21 (1967}, 204-219.

L.E. DICKSON, Cyclotomy whan e is composite, Trans. Amer. Math. Soc, 38 (1935), 187-200.

K.G.J. JACOBr, De residuis cubicis commentatio numerosa, /. fur die reine und angew. Math., 2(1827), 66-69.

EMMA LEHMER, The quintic character of 2 and 3, Duke Math. J. 18 (1951), 11-18.

P.A. LEONARD AND K.S. WILLIAMS, The septic character of 2, 3, 5, and 7, Pacific J. Math. 52 (1974) 143-147.

P.A. LEONARD, B.C. MORTIMER AND K.S. WILLIAMS, The eleventh power character of 2, to appear in Jour, fur reine und angew Math.

T. STORER, Cyclotomy and difference sets, Markham Publishing Co. (Chicago)8. K.S. WILLIAMS, 3 as a ninth power, Math. Scand 35 (1974), 309-317.