Some of My Favorite Problems and Results

  • Paul Erdős
Part of the Algorithms and Combinatorics book series (AC, volume 13)


Problems have always been essential part of my mathematical life. A well chosen problem can isolate an essential difficulty in a particular area, serving as a benchmark against which progress in this area can be measured. An innocent looking problem often gives no hint as to its true nature. It might be like a “marshmallow,” serving as a tasty tidbit supplying a few moments of fleeting enjoyment. Or It might be like an “acorn,” requiring deep and subtle new insights from which a mighty oak can develop.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. B. Bollobás, Extremal Graphy Theory, Academic Press, London, 1978.Google Scholar
  2. S. L. G. Choi, Covering the set of integers by congruence classes of distinct moduli, Mathematics of Computation 25 (1971), 885–895.MathSciNetMATHCrossRefGoogle Scholar
  3. R. Crocker, On the sum of a prime and two powers of two, Pacific J. Math. 36 (1971), 103–107.MathSciNetMATHGoogle Scholar
  4. H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, Springer-Verlag, New York, 1991.MATHCrossRefGoogle Scholar
  5. P. D. T. A. Elliot, Probabilistic Number Theory I, Mean-Value Theorems, Springer-Verlag, New York, 1979.Google Scholar
  6. P. D. T. A. Elliot, Probabilistic Number Theory II. Central Limit Theorems, Springer-Verlag, New York, 1980.Google Scholar
  7. P. Erdős, On sets of distances of n points, Amer. Math. Monthly 53 (1946), 248–250.MathSciNetCrossRefGoogle Scholar
  8. P. Erdős, On integers of the form 2k + p and some related problems, Summa Brasiliensis Math. II (1950), 113–123.Google Scholar
  9. P. Erdős and R. Rado, Intersection theorems for systems of sets, J. London Math. Soc. 35 (1960), 85–90.MathSciNetCrossRefGoogle Scholar
  10. P. Erdős and R. Rado, Intersection theorems for systems of sets II, J. London Math. Soc. 44 (1969), 467–479.MathSciNetCrossRefGoogle Scholar
  11. P. Erdős, The Art of Counting, J. Spencer, ed., MIT Press, Cambridge, MA, 1973.Google Scholar
  12. P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, Monograph 28, l’Enseignement Math., 1980.Google Scholar
  13. P. Erdos and G. Purdy, Combinatorial geometry, in Handbook of Combinatorics, R. L. Graham, M. Grötschel and L. Lovász, eds., North Holland, Amsterdam, 1994.Google Scholar
  14. P. X. Gallagher, Primes and powers of 2, Invent. Math. 29 (1975), 125–142.MathSciNetMATHCrossRefGoogle Scholar
  15. R. L. Graham, B. Rothschild and J. Spencer, Ramsey Theory, 2nd ed., Wiley, New York, 1990.MATHGoogle Scholar
  16. R. K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, New York, 1981.MATHGoogle Scholar
  17. H. Halberstam and K. F. Roth, Sequences, Springer-Verlag, New York, 1983.MATHGoogle Scholar
  18. R. R. Hall and G. Tenenbaum, Divisors, Cambridge University Press, Cambridge, 1988.MATHCrossRefGoogle Scholar
  19. J. Nešetřil and V. Rodi Mathematics of Ramsey Theory, Alg. and Comb. 5, Springer, New York, 1990.Google Scholar
  20. N. P. Romanoff, Über einige Sätze der additiven Zahlentheorie, Math. Annale 109 (1934), 668–678.MathSciNetCrossRefGoogle Scholar
  21. M. Simonovits, Extremal Graph Theory in Selected Topics in Graph Theory, L. Beineke and R. J. Wilson, eds., vol. 2, Academic Press, New York, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Paul Erdős
    • 1
  1. 1.Mathematical InstituteHungarian Academy of SciencesHungary

Personalised recommendations