Indices

problem
Favourite

Perfectly Square

Age

14 to 16

Challenge level

2 out of 3

The sums of the squares of three related numbers is also a perfect square - can you explain why?
problem
Favourite

Mega Quadratic Equations

Age

14 to 18

Challenge level

1 out of 3

What do you get when you raise a quadratic to the power of a quadratic?
problem
Favourite

Negative Powers

Age

14 to 18

Challenge level

2 out of 3

What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?
problem
Favourite

How Many Solutions?

Age

16 to 18

Challenge level

1 out of 3

Find all the solutions to the this equation.
problem
Favourite

Sums of Squares

Age

16 to 18

Challenge level

1 out of 3

Can you prove that twice the sum of two squares always gives the sum of two squares?
problem
Favourite

Telescoping Series

Age

16 to 18

Challenge level

2 out of 3

Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
problem
Favourite

Climbing Powers

Age

16 to 18

Challenge level

2 out of 3

Does it make any difference how we write powers of powers?
problem
Favourite

Giants

Age

16 to 18

Challenge level

2 out of 3

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
problem
Favourite

Tens

Age

16 to 18

Challenge level

2 out of 3

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?
problem

Novemberish

Age

14 to 16

Challenge level

1 out of 3

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.