previous up next
Go backward to Example
Go up to Top
Go forward to Example
RISC-Linz logo

Example (Continued)

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

(3) 3a = n3+2n.

We therefore have

(n+1)3+2(n+1) =
(n3 + 3n2 + 3n + 1) + (2n+2) =
(n3 + 2n) + (3n2 + 3n + 3) = (3)
3a + 3(n2 + n + 1) =
3(a + n2 + n + 1)
which implies (2) by definition of |.
Author: Wolfgang Schreiner
Last Modification: November 24, 1999

previous up next