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Old Nuts

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

Mod 7

Find the remainder when 3^{2001} is divided by 7.

Prime AP

What can you say about the common difference of an AP where every term is prime?

Purr-fection

Age 16 to 18 Challenge Level:

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

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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