Number Theory
# Basic Applications of Modular Arithmetic

John and Amy have \(48\) and \(51\) quarters, respectively. If they combine all of their quarters and change as much as possible into dollar bills, how many quarters will be left?

Note: There are 4 quarters in a dollar.

What is the sum of all positive prime numbers \(x\) such that \(x^2+2\) is also a prime?