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Double Time

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.


What is the smallest perfect square that ends with the four digits 9009?


Age 16 to 18 Short Challenge Level:

Choose any whole number $n$, calculate $n^3 + 11n$, and divide by 6.

For what values of $n$ is your answer a whole number?
Can you explain why?
Did you know ... ?
Modular arithmetic is widely used to verify automatically whether a number has been correctly entered to a system. Each identification number (e.g. for passports, bank accounts, credit cards, ISBN book numbers and so on) obeys a rule which makes it easy to check (most of the time) whether or not the number has been copied correctly. For this reason such numbers are also called check codes.