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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.

Basic Applications of Modular Arithmetic: Level 2 Challenges

         

The number of students in a school is between 500 and 600. If we group them into groups of 12, 20, 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 \(11?\)

What is the remainder when \(\Huge \color{red}{12}^{\color{green}{34}^{\color{blue}{56}^{\color{brown}{78}}}}\) is divided by \(\color{indigo}{90}?\)

What is the smallest positive integer which is a multiple of 7, yet it gives a remainder of 1 when divided by any of 2, 3, 4, 5, or 6?

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