Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  264.10016
Autor:  Erdös, Paul; Szemeredi, E.
Title:  On the number of solutions of m = sumi = 1k xik. (In English)
Source:  Analytic Number Theory, Proc. Sympos. Pure Math. 24, St. Louis Univ. Missouri 1972, 83-90 (1973).
Review:  [For the entire collection see Zbl 258.00004.]
The authors restrict the xi to be in ascending order, and included in {a1, ... ,a\ell }, where a1 < a2 < ..., and \ell > c1n, c1 a positive constant, n a positive integer. They then seek to choose m so that the equation of title has at least t solutions. They prove that such a choice is possible if n > n0(c1,t). They discuss many related results and conjectures, and give a number of references.
Reviewer:  G.L.Watson
Classif.:  * 11D41 Higher degree diophantine equations
                   11P99 Additive number theory

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