The equation $x^2+2=y^3$ looks nearly quadratic. What integer solutions can you find?

From this sum of powers, can you find the sum of the indices?

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

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

The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

Powers of numbers might look large, but which of these is the largest...

The sum of three square numbers equals $121$. What can those numbers be...

Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

How many integers n, between 1 and 100 inclusive, have the property that n^n is a square number?