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**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 a_{1},...,a_{n} are different positive integers, and n \geq 3 · 2^{k-1}, then the numbers a_{i}+a_{j}(i,j = 1,2,...,n) cannot all be composed only of k given primes.

2. If a_{1} < ... < a_{k+1} are positive integers, and b > a^{k}_{k+1}, then the numbers a_{i}+b (i = 1,2,...,k+1) cannot all be composed of only k given primes. On p.610, line 8 from below, read p^{\alphak}_{k} for p^{\alphak-1}_{k-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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