# Math Help - Another not integer number

1. ## Another not integer number

n is a integer number .
Prove that number $\sqrt[3]{3n^{2}+3n+7}$ is not
integer number .

2. Originally Posted by dhiab
n is a integer number .
Prove that number $\sqrt[3]{3n^{2}+3n+7}$ is not
integer number .
A perfect cube must be congruent to 0, 1, or 8 (mod 9).

Here is a table of n and its corresponding $3n^2+3n+7$ (mod 9).

0, 7
1, 4
2, 7
3, 7
4, 4
5, 7
6, 7
7, 4
8, 7

This list is exhaustive, and constitutes a proof.