Prove that ` 2222^(5555) + 5555^(2222) ` is
divisible by 7 .

Explanation

To prove that \( 2222^{5555} + 5555^{2222} \) is divisible by 7, we can use modular arithmetic. We will evaluate both terms modulo 7.

### Step 1: Calculate \( 2222 \mod 7 \)

First, we find \( 2222 \mod 7 \):
\[ 2222 \div 7 = 317 \quad \text{(integer part)} \]
...