## Twenty-fourth power residue difference sets

HTML articles powered by AMS MathViewer

- by Ronald J. Evans PDF
- Math. Comp.
**40**(1983), 677-683 Request permission

## Abstract:

It is proved that if*p*is a ${\text {prime}} \equiv 1\;\pmod 24$ such that either 2 is a cubic residue or 3 is a quartic residue $\pmod p$, then the twenty-fourth powers $\pmod p$ do not form a difference set or a modified difference set.

## References

- Leonard D. Baumert,
*Cyclic difference sets*, Lecture Notes in Mathematics, Vol. 182, Springer-Verlag, Berlin-New York, 1971. MR**0282863** - L. D. Baumert and H. Fredricksen,
*The cyclotomic numbers of order eighteen with applications to difference sets*, Math. Comp.**21**(1967), 204–219. MR**223322**, DOI 10.1090/S0025-5718-1967-0223322-5 - Bruce C. Berndt and Ronald J. Evans,
*Sums of Gauss, Jacobi, and Jacobsthal*, J. Number Theory**11**(1979), no. 3, S. Chowla Anniversary Issue, 349–398. MR**544263**, DOI 10.1016/0022-314X(79)90008-8 - S. Chowla,
*A property of biquadratic residues*, Proc. Nat. Acad. Sci. India Sect. A**14**(1944), 45–46. MR**14119** - Ronald J. Evans,
*Bioctic Gauss sums and sixteenth power residue difference sets*, Acta Arith.**38**(1980/81), no. 1, 37–46. MR**574123**, DOI 10.4064/aa-38-1-37-46
R. J. Evans, "Table of cyclotomic numbers of order twenty-four," - Emma Lehmer,
*On residue difference sets*, Canad. J. Math.**5**(1953), 425–432. MR**56007**, DOI 10.4153/cjm-1953-047-3 - Henry B. Mann,
*Addition theorems: The addition theorems of group theory and number theory*, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1965. MR**0181626** - J. B. Muskat,
*The cyclotomic numbers of order fourteen*, Acta Arith.**11**(1965/66), 263–279. MR**193081**, DOI 10.4064/aa-11-3-263-279 - Joseph B. Muskat and Albert L. Whiteman,
*The cyclotomic numbers of order twenty*, Acta Arith.**17**(1970), 185–216. MR**268151**, DOI 10.4064/aa-17-2-185-216 - Thomas Storer,
*Cyclotomy and difference sets*, Lectures in Advanced Mathematics, No. 2, Markham Publishing Co., Chicago, Ill., 1967. MR**0217033** - Albert Leon Whiteman,
*The cyclotomic numbers of order sixteen*, Trans. Amer. Math. Soc.**86**(1957), 401–413. MR**92807**, DOI 10.1090/S0002-9947-1957-0092807-7 - Albert Leon Whiteman,
*The cyclotomic numbers of order ten*, Proc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, pp. 95–111. MR**0113851** - A. L. Whiteman,
*The cyclotomic numbers of order twelve*, Acta Arith.**6**(1960), 53–76. MR**118709**, DOI 10.4064/aa-6-1-53-76

*Math. Comp.*, v. 35, 1980, pp. 1036-1038; UMT file

**12**[

**9.10**], 98 pp.

## Additional Information

- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp.
**40**(1983), 677-683 - MSC: Primary 12C20; Secondary 05B10, 10G05, 10L05
- DOI: https://doi.org/10.1090/S0025-5718-1983-0689481-4
- MathSciNet review: 689481