| Pollock's conjectures are two closely related unproven conjectures in additive number theory. According to Pollock's octahedral numbers conjecture, every positive integer is the sum of at most seven octahedral numbers, whereas according to Pollock's tetrahedral numbers conjecture, every positive integer is the sum of at most seven tetrahedral 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 part of a generalization of Fermat's polygonal number theorem to three-dimensional figurate numbers, also called polyhedral numbers. |
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