Tower of 31 part 5 (For Nihar 2)

n=15x31n \sum_{n=1}^5 x^{31n}

Nihar was working on a problem where he found following pattern for x31nx^{31n} where n=1,2,3,4,5n=1,2,3,4,5. Find the last 3 digits of the summation above when x=31x=31.

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