The sums of the squares of three related numbers is also a perfect square - can you explain why?
What do you get when you raise a quadratic to the power of a quadratic?
What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?
Find all the solutions to the this equation.
Can you prove that twice the sum of two squares always gives the sum of two squares?
Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
Does it make any difference how we write powers of powers?
Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
