Reminder when (5)^55 is divided by 3
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Explanation:
5^1 ÷ 3 leaves reminder 2
5^2 ÷ 3 leaves reminder 1
5^3 ÷ 3 leaves reminder 2
5^4 ÷ 3 leaves reminder 1
5^5 ÷ 3 leaves reminder 2
5^6 ÷ 3 leaves reminder 1
See the pattern. 5^n when n is odd leaves remainder 2. So 5^55 ÷ 3 will leave remainder 2.