Editing Centered cube number (section)

==Properties==
Because of the factorization {{math|(2''n'' + 1)(''n''<sup>2</sup> + ''n'' + 1)}}, it is impossible for a centered cube number to be a [[prime number]].<ref>{{Cite OEIS|A005898}}</ref>
The only centered cube numbers which are also the [[square number]]s are&nbsp;1 and 9,<ref>{{citation
 | last = Stroeker | first = R. J.
 | title = On the sum of consecutive cubes being a perfect square
 | journal = [[Compositio Mathematica]]
 | volume = 97
 | year = 1995
 | issue = 1–2
 | pages = 295–307
 | mr = 1355130
 | url = http://www.numdam.org/item?id=CM_1995__97_1-2_295_0}}.</ref><ref>{{citation|title=The Magic Numbers of the Professor|series=MAA Spectrum|first1=Owen|last1=O'Shea|first2=Underwood|last2=Dudley|publisher=Mathematical Association of America|year=2007|isbn=9780883855577|page=17|url=https://books.google.com/books?id=RC9304k036YC&pg=PA17}}.</ref> which can be shown by solving {{math|''x''<sup>2</sup> {{=}} ''y''<sup>3</sup> + 3''y'' }}, the only integer solutions being (x,y) from {(0,0), (1,2), (3,6), (12,42)}, By substituting a=(x-1)/2 and b=y/2, we obtain x^2=2y^3+3y^2+3y+1. This gives only (a,b) from {(-1/2,0), (0,1), (1,3), (11/2,21)} where a,b are half-integers.