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This is the **first** part of a TV documentary titled **Fermat’s Last Theorem**

made by the famous British science author, Simon Singh, along with John Lynch in 1996. More information on the documentary can be found here.

To quote Simon Singh,

*In 1996, working with John Lynch, I made a documentary about Fermat’s Last Theorem for the BBC series Horizon. It was 50 minutes of mathematicians talking about mathematics, which is not the obvious recipe for a TV blockbuster, but the result was a programme that captured the public imagination and which received critical acclaim.*

*The programme won the BAFTA for best documentary, a Priz Italia, other international prizes and an Emmy nomination – this proves that mathematics can be as emotional and as gripping as any other subject on the planet…*

You should definitely watch the opening scene which became very famous later on!

**Part 1:**

There are **five** parts in all. The rest of the four may be found by visiting YouTube.

The following fun problem was posed in one of the issues of the *American Mathematical Monthly* (if I am not wrong). I don’t remember the exact issue or the author, but here is the problem anyway.

Prove that is irrational for all and .

*Slick solution*: We could either use *Euclid’s* arguments or invoke the *rational root theorem* to prove the above statement. However, there is a slicker proof!

Assume, for the sake of contradiction, that , where and . Then, we have which implies . But this contradicts Fermat’s Last Theorem! And, we are done.

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