# Find and find again

**Number Theory**Level 5

\[\large{\displaystyle \sum_{n=0}^{100}n!}\]

If the last 2 digits of the sum above is \(x\), find the last 2 digits of:

\[\large{\displaystyle \sum_{m=0}^{100}m^x}\]

\[\large{\displaystyle \sum_{n=0}^{100}n!}\]

If the last 2 digits of the sum above is \(x\), find the last 2 digits of:

\[\large{\displaystyle \sum_{m=0}^{100}m^x}\]

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