Products of shifted primes simultaneously taking perfect power values

Details Products of shifted primes simultaneously taking perfect power values Products of shifted primes simultaneously taking perfect power values

2010-08-11

arxiv.org/abs/1008.1978v2

Mathematics

Number Theory

Fixed typo in second paragraph; fixed typo in numerical value for c on the bottom of p.8; added reference [12] (cited after st

Scientific paper

Let $r \ge 2$ be an integer and let $A$ be a finite, nonempty set of nonzero integers. We will obtain a lower bound for the number of squarefree integers $n$, up to $x$, for which the products $\prod_{p \mid n} (p+a)$ (over primes $p$) are perfect $r$th powers for all $a \in A$. Also, in the cases $A = \{-1\}$ and $A = \{+1\}$, we will obtain a lower bound for the number of such $n$ with exactly $r$ distinct prime factors.

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