Pollock's conjectures

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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 five 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.

References[edit]

  • Dickson, L. E. (June 7, 2005). History of the Theory of Numbers, Vol. II: Diophantine Analysis. Dover. pp. 22–23. ISBN 0-486-44233-0. 
  • Frederick Pollock (1850). "On the extension of the principle of Fermat's theorem on the polygonal numbers to the higher order of series whose ultimate differences are constant. With a new theorem proposed, applicable to all the orders". Abstracts of the Papers Communicated to the Royal Society of London 5: 922–924. JSTOR 111069. 

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