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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?


Age 16 to 18
Challenge Level

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