Indices

problem
Favourite

Negative Powers

Age

14 to 18

Challenge level

What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?
article
Public Key Cryptography

An introduction to coding and decoding messages and the maths behind how to secretly share information.
problem

Big, Bigger, Biggest

Age

16 to 18

Challenge level

Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?
problem
Favourite

Sums of Squares

Age

16 to 18

Challenge level

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

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

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

Giants

Age

16 to 18

Challenge level

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

Powerful Factors

Age

16 to 18

Challenge level

Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.
problem
Favourite

Tens

Age

16 to 18

Challenge level

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

Cube Roots

Age

16 to 18

Challenge level

Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.