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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.
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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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.
