Go backward to ExampleGo up to TopGo forward to Example |

By (1) and definition of | we have some `a` in **N** such that

(3) 3a=n^{3}+2n.

We therefore have

which implies (2) by definition of |.

( n+1)^{3}+2(n+1)= ( n^{3}+ 3n^{2}+ 3n+ 1) + (2n+2)= ( n^{3}+ 2n) + (3n^{2}+ 3n+ 3)= (3) 3a+ 3(n^{2}+n+ 1)= 3(a+n^{2}+n+ 1)

Author: Wolfgang Schreiner

Last Modification: November 24, 1999