Products of shifted primes simultaneously taking perfect power values

2010/08/11 by Freiberg, Tristan
#FOS: Mathematics #Number Theory (math.NT) #Primary 11N25 #Secondary 11A25

paper · doi:10.48550/arxiv.1008.1978

Abstract

Let r ≥ 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 ∏_{p | n} (p+a) (over primes p) are perfect rth powers for all a ∈ 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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