2 citations · 3 across the 8 of their papers we have counts for
9 papers
Elated Numbers
N. Bradley Fox, Nathan H. Fox, Helen G. Grundman +3
For a base , the -elated function, , maps a positive integer written in base to the product of its leading digit and the sum of the squares of its digits.…
Gaussian Happy Numbers
Breeanne Baker Swart, Susan Crook, Helen G. Grundman +1
This paper extends the concept of a -happy number, for , from the rational integers, , to the Gaussian integers, . We investigate the fixed…
Fixed Points of Augmented Generalized Happy Functions II: Oases and Mirages
Breeanne Baker Swart, Susan Crook, Helen G. Grundman +3
An augmented generalized happy function maps a positive integer to the sum of the squares of its base digits plus . For and , a …
Sequences of Consecutive Happy Numbers in Negative Bases
Helen G. Grundman, Pamela E. Harris
For and , let be the function taking an integer to the sum of the -powers of the digits of its base expansion…
Fixed Points of Augmented Generalized Happy Functions
Breeanne Baker Swart, Kristen A. Beck, Susan Crook +4
An augmented generalized happy function maps a positive integer to the sum of the squares of its base digits plus . In this paper, we study various properties of…
Augmented generalized happy functions
Breeanne Baker Swart, Kristen A. Beck, Susan Crook +4
An augmented happy function, maps a positive integer to the sum of the squares of its base- digits and a non-negative integer . A positive integer is in a cyc…
On the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5
Eva G. Goedhart, Helen G. Grundman
We prove that for each odd prime p, positive integer alpha, and non-negative integers beta and gamma, the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5 has…
On the Diophantine equation N X^2 + 2^L 3^M = Y^N
Eva G. Goedhart, Helen G. Grundman
We prove that the Diophantine equation N X^2 + 2^L 3^M = Y^N has no solutions (N,X,Y,L,M) in positive integers with N > 1 and gcd(NX,Y) = 1, generalizing results of Luca, Wang and…
Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory
Helen Grundman, Jennifer Johnson-Leung, Kristin Lauter +3
Bruinier and Yang conjectured a formula for an intersection number on the arithmetic Hilbert modular surface, CM(K).T_m, where CM(K) is the zero-cycle of points corresponding to ab…