## A Remainder Question

What is the remainder when 2222^5555 + 5555^2222 Is divided by 8? A Solution: Firstly, 2222 = 277 x 8 + 6 and 5555 = 694 x 8 + 3. So 2222^5555 + 5555^2222 has the “same” remainder when divided by 8 as 6^5555 + 3^2222. Now consider the “remainder” when powers of 6...

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