# Another not integer number

• May 27th 2010, 12:41 PM
dhiab
Another not integer number
n is a integer number .
Prove that number http://latex.codecogs.com/gif.latex?...]{3n^{2}+3n+7} is not
integer number .
• May 27th 2010, 01:28 PM
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Quote:

Originally Posted by dhiab
n is a integer number .
Prove that number http://latex.codecogs.com/gif.latex?...7B2%7D+3n+7%7D 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.