Article ID Journal Published Year Pages File Type
5772615 Journal of Number Theory 2017 7 Pages PDF
Abstract
For a positive integer n and a fixed positive integer q, let Cn=∏k=1n(k3+q3). We prove that Cn is not a powerful number if n≥max⁡{q,1198−q}, using some basic estimates on primes in arithmetic progressions. As applications of our main results, we discuss the powerfulness of Cn for 1≤q≤10.
Keywords
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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