### 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.

### Purr-fection

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

# Dirisibly Yours

##### Age 16 to 18 Challenge Level:

We wonder who can find and explain the shortest and neatest proof that

$5^{2n+1} + 11^{2n+1} + 17^{2n+1}$

is divisible by 33 for every non negative integer n .