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We prove by induction on `n`

forallninN: 3 |n^{3}+2n

The induction base holds because 3 | 0 and 0= 0^{3}+2*0.

We take arbitrary `n` in **N** and assume

(1) 3 |n^{3}+2n.

We have to show

(2) 3 | (n+1)^{3}+2(n+1).

Author: Wolfgang Schreiner

Last Modification: November 24, 1999