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11B: Sequences and Sets (including Fibonacci,...)


This is largely the study of arithmetic properties of well-known sets of integers: binomial coefficients, Fibonacci numbers, and so on. More generally one looks at sequences defined recursively, say, and inquires about their congruence properties, primality, etc. (Questions about rate of growth, for example, are more likely considered in section 40: Sequences (of real numbers).

This area includes a number of Erdös-like topics: Covering congruences, additive bases for the integers, van der Waerden's theorem on arithmetic progressions, etc.


Applications and related fields


Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

A nice survey of related results is in Erdös, P.; Graham, R. L.: "Old and new problems and results in combinatorial number theory", Université de Genève, L'Enseignement Mathématique, Geneva, 1980. 128pp.

"A primer for the Fibonacci numbers", edited by Marjorie Bicknell and Verner E. Hoggatt, Jr. The Fibonacci Association, San Jose State University, San Jose, Calif., 1972. 173 pp. MR50#12906

Bicknell, Marjorie: "A primer on the Pell sequence and related sequences", Fibonacci Quart. 13 (1975), no. 4, 345--349. MR52#8018

Some texts in combinatorics include quite a bit of "combinatorial number theory", including

Online arithmetic properties of binomial coefficients [Andrew Granville]

See also the references for number theory in general.

Software and tables

Other web sites with this focus

Selected topics at this site

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Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org