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.
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.