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198:(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".
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The numbers that are not the sum of at most 4 tetrahedral numbers are given by the sequence 17, 27, 33, 52, 73, ..., (sequence
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308:"Beweis des Satzes, daß sich eine jede ganze Zahl als Summe von höchstens neun positiven Kuben darstellen läßt"
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This conjecture has been proven for all but finitely many positive integers.
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Elessar Brady, Zarathustra (2016). "Sums of seven octahedral numbers".
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Abstracts of the Papers
Communicated to the Royal Society of London
386:"A Proof of Pollock's Conjecture on Centered Nonagonal Numbers"
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The cube numbers case was established from 1909 to 1912 by
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49:. These conjectures are a partial extension of the
136:: Every positive integer is the sum of at most 11
113:: Every positive integer is the sum of at most 9
98:: Every positive integer is the sum of at most 7
144:This conjecture was confirmed as true in 2023.
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134:Pollock centered nonagonal numbers conjecture
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252:Journal of the London Mathematical Society
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67:Pollock tetrahedral numbers conjecture
347:"Bemerkungen zum Waringschen Problem"
96:Pollock octahedral numbers conjecture
27:Conjectures in additive number theory
18:Pollock octahedral numbers conjecture
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41:. They were first stated in 1850 by
491:Unsolved problems in number theory
57:, also called polyhedral numbers.
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170:History of the Theory of Numbers
172:, Vol. II: Diophantine Analysis
111:Pollock cube numbers conjecture
51:Fermat polygonal number theorem
390:The Mathematical Intelligencer
384:Kureš, Miroslav (2023-10-27).
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439:. You can help Knowledge by
61:Statement of the conjectures
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398:10.1007/s00283-023-10307-0
138:centered nonagonal numbers
174:. Dover. pp. 22–23.
345:Kempner, Aubrey (1912).
73:is the sum of at most 5
501:Additive number theory
435:-related article is a
230:"Pollock's Conjecture"
39:additive number theory
351:Mathematische Annalen
312:Mathematische Annalen
53:to three-dimensional
43:Sir Frederick Pollock
31:Pollock's conjectures
33:are closely related
506:Number theory stubs
274:10.1112/jlms/jdv061
75:tetrahedral numbers
363:10.1007/BF01456723
324:10.1007/BF01450913
227:Weisstein, Eric W.
100:octahedral numbers
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304:Wieferich, Arthur
254:. Second Series.
196:Frederick Pollock
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206:: 922–924.
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69:: Every
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