Number Theory
# Basic Applications of Modular Arithmetic

Find the remainder when \(70!\) is divided by \(5183\).

Note: Don't use a computational device!

\[ \large \displaystyle\sum_{k=0}^{1007!+1}{10^k}\]

Find the remainder when the summation above is divided by the summation below.

\[ \large \displaystyle\sum_{k=0}^{1008}{10^k} \]

\[\Huge 6^{6^{6^{6^{6^6}}}}\]

Find the \(6^\text{th}\) last digit from the right of the decimal representation of the above number.

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