Efficient Algorithms for Decomposing Integers as Sums of Few Tetrahedral Numbers

Tong-Nong Lin, Yu-Cheng Lin, Cheng-Chen Tsai, Meng-Tsung Tsai, Shih-Yu Tsai

Abstract: Pollock conjectures that every natural number can be expressed as a sum of at most five tetrahedral numbers. It remains unknown whether this conjecture holds, and Watson proved that sums of at most eight tetrahedral numbers suffice to express all natural numbers.