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

Explanation

To prove that \( 2222^{5555} + 5555^{2222} \) is divisible by 7, we will use modular arithmetic and properties of exponents.

### Step 1: Find the remainders of \( 2222 \) and \( 5555 \) when divided by \( 7 \).

1. **Calculate \( 2222 \mod 7 \)**:
\[ 2222 \div 7 = 317 \quad \text{(integer part)} \]
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