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 each term modulo 7 and then check if their sum is congruent to 0 modulo 7.

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

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