Twenty-fourth power residue difference sets

Author:
Ronald J. Evans

Journal:
Math. Comp. **40** (1983), 677-683

MSC:
Primary 12C20; Secondary 05B10, 10G05, 10L05

MathSciNet review:
689481

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that if *p* is a such that either 2 is a cubic residue or 3 is a quartic residue , then the twenty-fourth powers do not form a difference set or a modified difference set.

**[1]**Leonard D. Baumert,*Cyclic difference sets*, Lecture Notes in Mathematics, Vol. 182, Springer-Verlag, Berlin-New York, 1971. MR**0282863****[2]**L. D. Baumert and H. Fredricksen,*The cyclotomic numbers of order eighteen with applications to difference sets*, Math. Comp.**21**(1967), 204–219. MR**0223322**, 10.1090/S0025-5718-1967-0223322-5**[3]**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**, 10.1016/0022-314X(79)90008-8**[4]**S. Chowla,*A property of biquadratic residues*, Proc. Nat. Acad. Sci. India. Sect. A.**14**(1944), 45–46. MR**0014119****[5]**Ronald J. Evans,*Bioctic Gauss sums and sixteenth power residue difference sets*, Acta Arith.**38**(1980/81), no. 1, 37–46. MR**574123****[6]**R. J. Evans, "Table of cyclotomic numbers of order twenty-four,"*Math. Comp.*, v. 35, 1980, pp. 1036-1038; UMT file**12**[**9.10**], 98 pp.**[7]**Emma Lehmer,*On residue difference sets*, Canadian J. Math.**5**(1953), 425–432. MR**0056007****[8]**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****[9]**J. B. Muskat,*The cyclotomic numbers of order fourteen*, Acta Arith.**11**(1965/1966), 263–279. MR**0193081****[10]**Joseph B. Muskat and Albert L. Whiteman,*The cyclotomic numbers of order twenty*, Acta Arith.**17**(1970), 185–216. MR**0268151****[11]**Thomas Storer,*Cyclotomy and difference sets*, Lectures in Advanced Mathematics, No. 2, Markham Publishing Co., Chicago, Ill., 1967. MR**0217033****[12]**Albert Leon Whiteman,*The cyclotomic numbers of order sixteen*, Trans. Amer. Math. Soc.**86**(1957), 401–413. MR**0092807**, 10.1090/S0002-9947-1957-0092807-7**[13]**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****[14]**A. L. Whiteman,*The cyclotomic numbers of order twelve*, Acta Arith.**6**(1960), 53–76. MR**0118709**

Retrieve articles in *Mathematics of Computation*
with MSC:
12C20,
05B10,
10G05,
10L05

Retrieve articles in all journals with MSC: 12C20, 05B10, 10G05, 10L05

Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1983-0689481-4

Keywords:
Power residue difference sets,
cyclotomic numbers,
Gauss and Jacobi sums

Article copyright:
© Copyright 1983
American Mathematical Society