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Number Theory

Basic Applications of Modular Arithmetic

Concept Quizzes

Chinese Remainder Theorem
Fermat's Little Theorem
Wilson's Theorem
Modular Arithmetic - Word Problems
Modular Arithmetic - Problem Solving
Practical Applications of Modular Arithmetic Warmup
Time Adjustments
Caesar Shift
Friday the 13th

Challenge Quizzes

Basic Applications of Modular Arithmetic: Level 2 Challenges
Basic Applications of Modular Arithmetic: Level 3 Challenges
Basic Applications of Modular Arithmetic: Level 4 Challenges

Modular Arithmetic - Word Problems

There are $81$ groups of $21$ students. When we regroup all of the students so that each group has $5$ members, how many students will be left without a group?

1 2 3 0

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by Brilliant Staff

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.

2 0 1 3

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by Brilliant Staff

November and December have $30$ and $31$ days, respectively. If November $1$ is the first day of the week, how many days of December are there in the last week?

6 4 5 0

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by Brilliant Staff

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

1 2 3 4 5 6 7

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by Brilliant Staff

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

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by Brilliant Staff

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