Sums of Two Generalized Tetrahedral Numbers
Keywords:
tetrahedral numbers; generalized tetrahedral numbers; figurate numbers; sums of figurate numbers; Waring's problem
Abstract
Expressing whole numbers as sums of figurate numbers, including tetrahedral numbers, is a longstanding problem in number theory. Pollock's tetrahedral number conjecture states that every positive integer can be expressed as the sum of at most five tetrahedral numbers. Here we explore a generalization of this conjecture to negative indices. We provide a method for computing sums of two generalized tetrahedral numbers up to a given bound, and explore which families of perfect powers can be expressed as sums of two generalized tetrahedral numbers.
Published
2022-12-23
How to Cite
Lycan, R., & Ponomarenko, V. (2022). Sums of Two Generalized Tetrahedral Numbers. The PUMP Journal of Undergraduate Research, 5, 206-217. Retrieved from https://journals.calstate.edu/pump/article/view/3329
Section
Articles
Copyright (c) 2022 Ron Lycan, Vadim Ponomarenko

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.