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On a problem in the elementary theory of numbers. (English) Zbl 0010.29401
The following two theorems are proved by elementary methods.
1. If $$a_1,...,a_n$$ are different positive integers, and $$n \geq 3 \cdot 2^{k-1}$$, 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 $$p^{\alpha_k}_k \text{ for } p^{\alpha_{k-1}}_{k-1}$$ on p.611, line 7, read ”that each one” for ”that one”.

MSC:
 11B83 Special sequences and polynomials
number theory
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