Any $n$ arithmetic progressions covering the first $2^{n}$ integers cover all integers
Authors:
R. B. Crittenden and C. L. Vanden Eynden
Journal:
Proc. Amer. Math. Soc. 24 (1970), 475-481
MSC:
Primary 10.05
DOI:
https://doi.org/10.1090/S0002-9939-1970-0258719-2
MathSciNet review:
0258719
Full-text PDF Free Access
References | Similar Articles | Additional Information
- Richard B. Crittenden and C. L. Vanden Eynden, A proof of a conjecture of Erdős, Bull. Amer. Math. Soc. 75 (1969), 1326–1329. MR 249351, DOI https://doi.org/10.1090/S0002-9904-1969-12415-8
- Pál Erdős, Remarks on number theory. IV. Extremal problems in number theory. I, Mat. Lapok 13 (1962), 228–255 (Hungarian, with English and Russian summaries). MR 195822 ---, Problems $29$ and $30$, Proc. Conf. Number Theory (Boulder, Colorado, 1963).
- P. Erdős, Extremal problems in number theory, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., Providence, R.I., 1965, pp. 181–189. MR 0174539 John Selfridge, Research announcement, Amer. Math. Soc. Annual Meeting (New Orleans, 1969). ---, On congruences covering consecutive integers, Acta Arith. (to appear).
- Sherman K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289–294. MR 93493, DOI https://doi.org/10.1007/BF01343822
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10.05
Retrieve articles in all journals with MSC: 10.05
Additional Information
Article copyright:
© Copyright 1970
American Mathematical Society