Modular arithmetic

What is the units digit for the number 123^(456) ?

What are the possible remainders when the 100-th power of an integer is divided by 125?

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

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

What is the remainder when 2^{164}is divided by 7?

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.

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.

Here are many ideas for you to investigate - all linked with the number 2000.