Maths on a Mug 9

Fermat’s Last Theorem is a celebrated result in mathematics, simply it says that:

There are no three positive integers \(a,b,c\) such that \(a^n+b^n=c^n\) for any value of \(n>2\).

For the value \(n=2\) this is the well known Pythagoras theorem. Fermat’s Last Theorem is easy to state, but which was fiendishly hard to prove. It was first stated by Fermat in 1637 and took until May of 1995 to be finally proved by Sir Andrew Wiles.

However there is a fun ‘near-miss’ solution which was shown in the Simpsons, and is on the mug this morning. If you type this solution into your handy pocket calculator you will think you’ve found a counterexample:

\[3987^{12}+4365^{12}=4472^{12}\]

However, the numbers are so large (e.g. \(4472^{12}=63976656348486725806862358322168575784124416\)) that your calculator doesn’t actually work out the whole values and there is a ‘rounding error’, which is what gives rise to the apparent counterexample, perfectly highlighted by The Simpsons.

An excellent video briefly explaining this is available here:

It turns out The Simpsons is riddled with mathematical facts and quirks, and these are brilliant captured in The Simpsons and Their Mathematical Secrets by Simon Singh.

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