## Task A-2.3.

Determine all triples of prime numbers $(p, q, r)$ for which

$$
p^{q}=r-1
$$
Scoring: 1 point is awarded for concluding that $r$ is not 2, and another 2 points for determining that $p=2$. 1 point is awarded for the case $q=2$, and 3 points for eliminating the case $q>2$.

A written solution of $(2,2,5)$ earns 1 point even if it is not justified.