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

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.

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

What does this number mean ?

Which order of $1, 2, 3$ and $4$ makes the highest value ?

Which makes the lowest ?