Pollock's conjectures


Pollock's conjectures are two closely related unproven conjectures in additive number theory. 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 a partial extension of the Fermat polygonal number theorem to three-dimensional figurate numbers, also called polyhedral numbers.
The numbers that are not the sum of at most 4 tetrahedral numbers are given by the sequence 17, 27, 33, 52, 73,..., of 241 terms, with 343867 being almost certainly the last such number.