TY - JOUR
AU - Lycan, Ron
AU - Ponomarenko, Vadim
PY - 2022/12/23
Y2 - 2024/07/22
TI - Sums of Two Generalized Tetrahedral Numbers
JF - The PUMP Journal of Undergraduate Research
JA - PUMP J. Undergrad. Res.
VL - 5
IS - 0
SE - Articles
DO - 10.46787/pump.v5i0.3329
UR - https://journals.calstate.edu/pump/article/view/3329
SP - 206-217
AB - <p>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.</p>
ER -