Merged into Pollock's conjectures 21:13, 17 January 2018 (UTC)
In additive number theory, Pollock's conjectures are unproven[1] conjectures that every positive integer is the sum of at most five tetrahedral numbers[2], and that every positive integer is the sum of at most seven octahedral numbers.[3] They were first stated in 1850 by Sir Frederick Pollock[3], 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.
References edit
- ^ Deza, Elena; Deza, Michael (2012). Figurate Numbers. World Scientific.
{{cite book}}: Cite has empty unknown parameter:|1=(help) - ^ Weisstein, Eric W. "Pollock's Conjecture". MathWorld.
- ^ a b 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.
Category:Additive number theory
Category:Conjectures
Category:Figurate numbers
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