User:Arthur Rubin/Pollock's conjectures

Merged into Pollock's conjectures 21:13, 17 January 2018 (UTC)

In additive number theory, Pollock's conjectures are unproven conjectures that every positive integer is the sum of at most five tetrahedral numbers, and that every positive integer is the sum of at most seven octahedral numbers. They were first stated in 1850 by Sir Frederick Pollock, better known as a lawyer and politician but also a contributor of papers on mathematics to the Royal Society. These conjectures are partial generalization of Fermat's polygonal number theorem to three dimensional figurate numbers, also called polyhedral numbers.