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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.

The number of students in a school is a positive integer and is between 500 and 600.

If we group them into groups of 20, 12, or 36 each, 7 students are always left over. How many students are in this school?

Find the remainder when \(2016!-2015!\) is divided by \(2017\).

You may use the fact that \(2017\) is prime.

What is the remainder when \({7}^{88}\) is divided by \(11?\)

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