Here is the given:

$\displaystyle n^2 -7n+12$ is non-negative integer whenever n is an integer with $\displaystyle n \geq 3$

Here is what i come up with:

Hypothesis: $\displaystyle P(k) = k^2 - 7k + 12$

Conclusion: $\displaystyle P(k+3) = (k+3)^2 - 7(k+3) + 12 > 0$