Number Theory
# Basic Applications of Modular Arithmetic

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 \(13?\)

**NOT** be expressed as \[x^2+y^2+5z^2 ?\]

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