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Products of shifted primes simultaneously taking perfect power values
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2012 (English)In: Journal of the Australian Mathematical Society, ISSN 1446-7887, E-ISSN 1446-8107, Vol. 92, no 2, 145-154 p.Article in journal (Refereed) Published
Abstract [en]

Let r be an integer greater than 1, and let A be a finite, nonempty set of nonzero integers. We obtain a lower bound for the number of positive squarefree integers n, up to x, for which the products Pi(p vertical bar n)(p + a) (over primes p) are perfect rth powers for all the integers a in A. Also, in the cases where A = {-1} and A = {+1}, we will obtain a lower bound for the number of such n with exactly r distinct prime factors.

Place, publisher, year, edition, pages
2012. Vol. 92, no 2, 145-154 p.
Keyword [en]
shifted primes, Euler's totient function, perfect powers
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-107637DOI: 10.1017/S1446788712000249ISI: 000311401300002Scopus ID: 2-s2.0-84870152916OAI: oai:DiVA.org:kth-107637DiVA: diva2:577932
Note

QC 20121218

Available from: 2012-12-17 Created: 2012-12-14 Last updated: 2017-12-06Bibliographically approved

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