2 citations · 2 across the 3 of their papers we have counts for
11 papers
On Zeckendorf-Niven numbers and arithmetic progressions
Kelly Lao, Steven J. Miller, Nicholas Rosa +4
A positive integer is Zeckendorf-Niven (respectively, Lucas-Niven) if it is divisible by the number of summands in its Zeckendorf decomposition (respectively, Lucas decomposition).…
Arithmetic progressions of integers that are relatively prime to their digital sums
Ryan Blau, Joshua Harrington, Sarah Lohrey +2
For an integer , we call a positive integer -anti-Niven if it is relatively prime to the sum of the digits in its base- representation. In this article, we investiga…
Every arithmetic progression contains infinitely many -Niven numbers
Joshua Harrington, Matthew Litman, Tony W. H. Wong
For an integer , a positive integer is called a -Niven number if it is a multiple of the sum of the digits in its base- representation. In this article, we show that…
Probabilistic chip-collecting games with modulo winning conditions
Joshua Harrington, Xuwen Hua, Xufei Liu +3
Let , , and be integers with . In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects chips or …
Covering systems with odd moduli
Joshua Harrington, Yewen Sun, Wing Hong Tony Wong
The concept of a covering system was first introduced by Erdős in 1950. Since their introduction, a lot of the research regarding covering systems has focused on the existence of c…
Residue sums of Dickson polynomials over finite fields
Thomas Brazelton, Joshua Harrington, Matthew Litman +1
Given a polynomial with integral coefficients, one can inquire about the possible residues it can take in its image modulo a prime . The sum over the distinct residues can somet…