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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?

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.