Euler Lucky Number/Examples/2

Example of Euler Lucky Number
The expression:
 * $n^2 + n + 2$

yields primes for $n = 0$ and for no other $n \in \Z_{\ge 0}$.

This demonstrates that $2$ (trivially) is a Euler lucky number.

Proof
Let $n > 0$.

Then:

and so is divisible by $2$.

[[Category:2]]