The difference between consecutive members of a difference set

Author:
E. Spence

Journal:
Proc. Amer. Math. Soc. **46** (1974), 150-154

MSC:
Primary 05B10

DOI:
https://doi.org/10.1090/S0002-9939-1974-0345843-2

MathSciNet review:
0345843

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a difference set so that for any there are exactly pairs such that . Suppose further that and write . The following two results are proved:

(i)

(ii)

**[1]**L. D. Baumert,*Cyclic difference sets*, Lecture Notes in Math., vol. 182, Springer-Verlag, Berlin and New York, 1971. MR**44**#97. MR**0282863 (44:97)****[2]**P. Erdös and P. Turán,*On a problem of Sidon in additive number theory, and on some related problems*, J. London Math. Soc.**16**(1941), 212-215. MR**3**, 270. MR**0006197 (3:270e)****[3]**C. Hooley,*On the difference of consecutive numbers prime to*, Acta Arith.**8**(1962/63), 343-347. MR**27**#5741. MR**0155807 (27:5741)****[4]**K. K. Norton,*On the distribution of th power residues and non-residues modulo*, J. Number Theory**1**(1969), 398-418. MR**40**#4223. MR**0250992 (40:4223)****[5]**H. J. Ryser,*Combinatorial mathematics*, Carus Math. Mono., no. 14, Wiley, New York. MR**0150048 (27:51)****[6]**J. Singer,*A theorem in finite projective geometry and some applications to number theory*, Trans. Amer. Math. Soc.**43**(1938), 377-385. MR**1501951**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
05B10

Retrieve articles in all journals with MSC: 05B10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0345843-2

Keywords:
Difference set

Article copyright:
© Copyright 1974
American Mathematical Society