## Fermat’s Last Theorem

The Pythagorean theorem says that in a right triangle, a² + b² = c². Now suppose we force the variables to be integers. So the solution a=3, b=4, c=5 is allowed, but a=1.5, b=2, c=2.5 is not allowed, even though it fits the equation. It can be shown that there are an infinite number of solutions with a, b, c all integers.

But what happens if we take this one step up? How many integer solutions are there to a³ + b³ = c³? The answer is none. The same happens with a⁴ + b⁴ = c⁴: no solutions.

a^n + b^n = c^n

In fact, Fermat’s Last Theorem states that for any exponent higher than 2, this equation has no integer solutions. This famous problem, conjectured in 1637, took nearly four centuries to solve, being proved finally by Andrew Wiles in 1995.