## 103. Math Puzzle 12/73

Is there a natural number $a>0$ for which the following equation holds:

$$
a^{n}+a^{n}=a^{n+1}
$$
Summarizing the left side and transforming the right side of the equation according to a power rule, one obtains $2 a^{n}=a^{n+1}$. After dividing by $a^{n}$, which is always unequal to 0, one immediately gets $a=2$.

There is exactly one natural number $a$, namely 2, that satisfies the equation mentioned above.