What is $\left(2^{10} + 3^{5}\right) \bmod 7$?

Explanation

1. 01

   $2^{3} = 8 \equiv 1$, so $2^{10} = (2^{3})^{3} \cdot 2 \equiv 2$. And $3^{5} = 243 = 7 \times 34 + 5$, so $3^{5} \equiv 5$.

2. 02

   $2 + 5 = 7 \equiv 0$.