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math.NT2023
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…
math.NT2023
Sums of Reciprocals of Recurrence Relations
Hao Cui, Xiaoyu Cui, Sophia C. Davis +7
There is a growing literature on sums of reciprocals of polynomial functions of recurrence relations with constant coefficients and fixed depth, such as Fibonacci and Tribonacci nu…
math.NT2022
Winning Strategies for Generalized Zeckendorf Game
Steven J. Miller, Eliel Sosis, Jingkai Ye
Zeckendorf proved that every positive integer can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence…