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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.

Purr-fection

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

Remainder Hunt

Age 16 to 18
Challenge Level

What are the possible remainders when the $100^{th}$ power of an integer is divided by $125$? To reduce the number of cases to be checked, express the number as $5p+q $ where $p $ and $q $ are integers and $q=1,2,3,4 $ and find the hundredth power using the Binomial Theorem.