Abstract
Problems have always been an 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
B. Bollobás, Extremal Grophy Theory, Academic Press, London, 1978.
S. L. G. Choi, Covering the set of integers by congruence classes of distinct moduli, Mathematics of Computation 25 (1971), 885–895.
R. Crocker, On the sum of a prime and two powers of two, Pacific J. Math. 36 (1971), 103–107.
H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, Springer-Verlag, New York, 1991.
P. D. T. A. Elliot, Probabilistic Number Theory I, Mean-Value Theorems, Springer-Verlag, New York, 1979.
P. D. T. A. Elliot, Probabilistic Number Theory II, Central Limit Theorems, Springer-Verlag, New York, 1980.
P. Erdős, On sets of distances of n points, Amer. Math. Monthly 53 (1946), 248–250.
P. Erdős, On integers of the form 2k + pand some related problems, Summa Brasiliensis Math. II (1950), 113–123.
P. Erdős and R. Rado, Intersection theorems for systems of sets, J. London Math. Soc. 35 (1960), 85–90.
P. Erdős and R. Rado, Intersection theorems for systems of sets II, J. London Math. Soc. 44 (1969), 467–479.
P. Erdős, The Art of Counting, J. Spencer, ed., MIT Press, Cambridge, MA, 1973.
P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, Monograph 28, l’Enseignement Math., 1980.
P. Erdős and G. Purdy, Combinatorial geometry, in Handbook of Combinatorics, R. L. Graham, M. Grötschel and L. Lovász, eds., North Holland, Amsterdam, 1994.
P. X. Gallagher, Primes and powers of 2, Invent. Math. 29 (1975), 125–142.
R. L. Graham, B. Rothschild and J. Spencer, Ramsey Theory, 2nd ed., Wiley, New York, 1990.
R. K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, New York, 1981.
H. Halberstam and K. F. Roth, Sequences, Springer-Verlag, New York, 1983.
R. R. Hall and G. Tenenbaum, Divisors, Cambridge University Press, Cambridge, 1988.
J. Nešetřil and V. Rödl, Mathematics of Ramsey Theory, Alg. and Comb. 5, Springer, New York, 1990.
N. P. Romanoff, Über einige Sätze der additiven Zahlentheorie, Math. Annalen 109 (1934), 668–678.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Erdős, P. (2013). Some of My Favorite Problems and Results. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős I. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7258-2_3
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7258-2_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-7257-5
Online ISBN: 978-1-4614-7258-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)