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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.

Problem Solving - Basic

         

What is the remainder of \(\displaystyle {1776}^{2011!}\) upon division by \(2000?\)

What is the remainder of \({22}!\) upon division by \(23?\)

What is the remainder of \(\displaystyle {144}^{10}\) upon division by \(13?\)

What is the remainder of \(m\) satisfying \[\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{33}=\frac{m}{33!}\] upon division by \(17 ?\)

For three integers \(x,\) \(y\) and \(z,\) which of the following can NOT be expressed as \[x^2+y^2+5z^2 ?\]

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