134 citations
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math.NT2017
A generalization of the practical numbers
Nicholas Schwab, Lola Thompson
A positive integer is practical if every can be written as a sum of distinct divisors of . One can generalize the concept of practical numbers by applying an arit…
math.NT2014★ 5 cited
Arithmetic functions at consecutive shifted primes
Paul Pollack, Lola Thompson
For each of the functions and every natural number , we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots…
math.NT2014★ 4 cited
Bounded gaps between primes in number fields and function fields
Abel Castillo, Chris Hall, Robert J. Lemke Oliver +2
The Hardy--Littlewood prime -tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs…