Sums of Two Generalized Tetrahedral Numbers

  • Ron Lycan San Diego State University
  • Vadim Ponomarenko San Diego State University
Keywords: tetrahedral numbers; generalized tetrahedral numbers; figurate numbers; sums of figurate numbers; Waring's problem


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.

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