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arXiv · 1008.1978

Products of shifted primes simultaneously taking perfect power values

Tristan Freiberg
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Abstract

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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Tristan Freiberg. 2010-08-11. Products of shifted primes simultaneously taking perfect power values. https://doi.org/10.1017/s1446788712000249

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