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More Mods

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

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Mod 3

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

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Novemberish

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.

Check Code Sensitivity

Stage: 4 Challenge Level: Challenge Level:1
Remember that to show that a result is not true, or that a method fails, you only have to find one counterexample, that is one case where it fails. To prove that a result is always true you need a completely general argument. No matter how many cases you give where the result is true that does not prove that it is always true.