Here's a little puzzle for you guys.

Find the smallest integers $\displaystyle a$ and $\displaystyle b$ that verify :

$\displaystyle a \in N$

$\displaystyle b \in N$

$\displaystyle 1 < a < b$

$\displaystyle a^2 \equiv a$ (mod $\displaystyle b^2$)

The answer is obvious, yet you have to think of it ...