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How many noughts are at the end of these giant numbers?

Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

Euler's Officers

How many different ways can you arrange the officers in a square?

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Age 14 to 16 Challenge Level:

What is the units digit for the number 123$^{456}$?