Indices

article
Public key cryptography

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

Age

11 to 14

Challenge level

The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?
problem
Maundy money

Age

11 to 14

Challenge level

How much money did the Queen give away in pence as a power of 2?
problem
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?
problem
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
Elevens

Age

16 to 18

Challenge level

Add powers of 3 and powers of 7 and get multiples of 11.
problem
Largest expression

Age

14 to 16

Challenge level

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?
problem
Powerful zeros

Age

14 to 16

Challenge level

How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?
problem
Perfectly square

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.