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More Mods

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

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.

Rachel's Problem

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

A Biggy

Age 14 to 16
Challenge Level

Find the smallest positive integer $N$ such that \[{N\over 2} \] is a perfect cube, \[{N\over 3} \] is a perfect fifth power and \[{N\over 5} \] is a perfect seventh power.
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