[1] They were first stated in 1850 by Sir Frederick Pollock,[1][2] better known as a lawyer and politician, but also a contributor of papers on mathematics to the Royal Society.
These conjectures are a partial extension of the Fermat polygonal number theorem to three-dimensional figurate numbers, also called polyhedral numbers.
[3] This conjecture has been proven for all but finitely many positive integers.
[4] The cube numbers case was established from 1909 to 1912 by Wieferich[5] and A. J.
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