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An Extension of a Theorem of D. H. Lehmer

机译：D. H. Lehmer的定理的延伸

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Given a set of primes q1 < q2 < ... < qt- let Q be the set of all numbers of the form qa11 qa22 ... qat, where ai > 0. Lelimer lias given necessary and sufficient conditions to determine when both of the integers S and S + k, with A' = 1, 2 or 4, belong to Q. In addition, he has provided upper bounds for the number of pairs of such integers contained in Q, and for the largest value of S. In this paper we investigate extensions of Lelnner's results to the case when k is an arbitrary positive integer.

机译：给定一组Primes Q1 0. Lelimer Lias给出了必要和充分的条件，以确定何时具有'= 1,2或4的整数S和S + k属于Q.此外，他为Q中包含的这种整数的成对数提供了上限，并且用于S的最大值。在本文中，当K是任意的正整数时，我们调查Lelnner的延伸结果。

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《Canadian Number Theory Association 》|2004年||共12页
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Lenny Jones;
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An Extension of a Theorem of D. H. Lehmer

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