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Question

Find the remainder when 33818^2 + 33819^2 + 33820^2 + 33821^2 + 33822^2is divided by 17.

Accepted Answer

Reducing each number modulo 17, we get align* &33818^2 + 33819^2 + 33820^2 + 33821^2 + 33822^2 & 5^2 + 6^2 + 7^2 + 8^2 + 9^2 & 255 & 0 17. align*