# Tower of 31 part 5 (For Nihar 2)

**Number Theory**Level 4

\[ \sum_{n=1}^5 x^{31n} \]

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

\[ \sum_{n=1}^5 x^{31n} \]

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

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