## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  010.29401
Autor:  Erdös, Paul; Turán, Pál
Title:  On a problem in the elementary theory of numbers. (In English)
Source:  Am. Math. Mon. 41, 608-611 (1934).
Review:  The following two theorems are proved by elementary methods.
1. If a1,...,an are different positive integers, and n \geq 3 · 2k-1, then the numbers ai+aj(i,j = 1,2,...,n) cannot all be composed only of k given primes.
2. If a1 < ... < ak+1 are positive integers, and b > akk+1, then the numbers ai+b (i = 1,2,...,k+1) cannot all be composed of only k given primes. On p.610, line 8 from below, read p\alphakk for p\alphak-1k-1 on p.611, line 7, read "that each one" for "that one".
Reviewer:  Davenport (Cambridge)
Classif.:  * 11B83 Special sequences of integers and polynomials
Index Words:  number theory

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