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More Mods

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

Mod 3

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


a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

Filling the Gaps

Age 14 to 16
Challenge Level

Well done to Christopher from Sale Grammar School who sent us this solution using modular arithmetic.