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.
Fac-finding
Age 14 to 16 Challenge Level
If factorial $100$ ($100!$) was rewritten as the product of its prime factors how many $2$s and how many $5$s would there be?
Along the way, confirm how many zeros are at the end of this large number and what the first digit to precede them is.