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N000ughty Thoughts

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.


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.


Age 14 to 16
Challenge Level


One of the challenges of this problem is the reading of a mathematical text for understanding

It would be interesting to investigate why superincreasing series are easier to deal with.

There is an article on Knapsack codes.