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# Basic Applications of Modular Arithmetic

Solve integer equations, determine remainders of powers, and much more with the power 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 \(6\)th last digit from the right of the decimal representation of the above number.

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