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Pollock's conjectures

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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 possible extension of the Fermat polygonal number theorem to three-dimensional figurate numbers, also called polyhedral numbers.

  • Pollock tetrahedral numbers conjecture: Every positive integer is the sum of at most five tetrahedral numbers.
  • Pollock octahedral numbers conjecture: Every positive integer is the sum of at most seven octahedral numbers.

    • References

    Pollock's conjectures Wikipedia
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