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Any $ n$ arithmetic progressions covering the first $ 2\sp{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
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  • [1] R. B. Crittenden and C. L. Vanden Eynden, A proof of a conjecture of Erdös, Bull. Amer. Math. Soc. 75 (1969), 1326-1329. MR 0249351 (40:2596)
  • [2] P. Erdös, Remarks on number theory. IV: Extremal problems in number theory. I, Mat. Lapok. 13 (1962), 228-255. (Hungarian) MR 33 #4020. MR 0195822 (33:4020)
  • [3] -, Problems $ 29$ and $ 30$, Proc. Conf. Number Theory (Boulder, Colorado, 1963).
  • [4] -, Extremal problems in number theory, Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc., Providence, R.I., 1965, p. 183. MR 30 #4740. MR 0174539 (30:4740)
  • [5] John Selfridge, Research announcement, Amer. Math. Soc. Annual Meeting (New Orleans, 1969).
  • [6] -, On congruences covering consecutive integers, Acta Arith. (to appear).
  • [7] S. K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289-294. MR 20 #17. MR 0093493 (20:17)

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DOI: https://doi.org/10.1090/S0002-9939-1970-0258719-2
Article copyright: © Copyright 1970 American Mathematical Society

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