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Purr-fection

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

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?

Prime AP

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

Mod 7

Age 16 to 18 Challenge Level:

Find the remainder when 3 2001 is divided by 7.