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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Modular Arithmetic

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Clock Arithmetic

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More Adventures with Modular Arithmetic

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Clock Squares

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Euler's Totient Function

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Public Key Cryptography

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Public Key Cryptography Interactivity

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An Introduction to Number Theory

## You may also like

### Making Sense of Statistics

### Integration as Area

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The problems in this feature introduce the idea of modular (or clock) arithmetic, and encourage you to explore the modular world. There are opportunities for noticing patterns and discovering some general rules which hold in this type of arithmetic.

You can build on these ideas when exploring our Public Key Cryptography Interactivity, and see how Public Keys are used to keep our personal information secure.

You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these problems.

The last day for sending in solutions to our live problems is Monday 17 May.

Age 11 to 18

Challenge Level

What happens if we change the rules and make the usual straight number line into a circle?

Age 14 to 18

Challenge Level

Investigate what happens when we add or multiply numbers using modular arithmetic.

Age 14 to 18

Challenge Level

Can you find a way of predicting the value of large square numbers with the help of our power modulo calculator?

Age 16 to 18

Challenge Level

How many numbers are there less than $n$ which have no common factors with $n$?

Age 16 to 18

An introduction to coding and decoding messages and the maths behind how to secretly share information.

Age 16 to 18

Here's a chance to simulate sending secret messages and trying to decode them.

Age 16 to 18

An introduction to some beautiful results in Number Theory.

*We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.*

This collection of problems has been put together to help you to explore and understand important ideas in statistics.

These problems invite you to explore integration as area, and use area integrals to solve problems.