# Modular Arithmetic

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.

### Clock Arithmetic

##### Age 11 to 18Challenge Level
What happens if we change the rules and make the usual straight number line into a circle?

### More Adventures with Modular Arithmetic

##### Age 14 to 18Challenge Level
Investigate what happens when we add or multiply numbers using modular arithmetic.

### Clock Squares

##### Age 14 to 18Challenge Level
Can you find a way of predicting the value of large square numbers with the help of our power modulo calculator?

### Euler's Totient Function

##### Age 16 to 18Challenge Level
How many numbers are there less than $n$ which have no common factors with $n$?

### Public Key Cryptography

##### Age 16 to 18
An introduction to coding and decoding messages and the maths behind how to secretly share information.

### Public Key Cryptography Interactivity

##### Age 16 to 18
Here's a chance to simulate sending secret messages and trying to decode them.

### An Introduction to Number Theory

##### 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.