Number Theory

Basic Applications of Modular Arithmetic

Modular Arithmetic - Word Problems

         

There are 8181 groups of 2121 students. When we regroup all of the students so that each group has 55 members, how many students will be left without a group?

John and Amy have 4848 and 5151 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.

November and December have 3030 and 3131 days, respectively. If November 11 is the first day of the week, how many days of December are there in the last week?

How many different values are there for 4n(mod7) 4 ^ n \pmod { 7} , as nn ranges over all positive integers?

What is the sum of all positive prime numbers xx such that x2+2x^2+2 is also a prime?

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