What is the remainder when the sum 1^{5}+2^{5}+3^{5}+4^{5}+5^{5} is divided by 4?

Explanation

Find remainder of each term when divided by 4: 1^5 \equiv 1, 2^5 \equiv 0, 3^5 \equiv (-1)^5 \equiv -1 \equiv 3, 4^5 \equiv 0, 5^5 \equiv 1^5 \equiv 1. Summing them up: 1 + 0 + 3 + 0 + 1 = 5. Dividing 5 by 4 gives a remainder of 1.

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