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Do you understand the difference between conjecture and theorem? It is crucial you do before you start thinking about Fermat's conjecture.

Conjecture is a kind of guesswork: you make a judgment based on some inconclusive or incomplete evidence and you call it a conjecture. Or you make a kind of statement, but this is based only on your opinion, or again, guesswork - this is a conjecture once again. You may be proved right or wrong. Sometimes it may take centuries for people to prove you either right or wrong. If they prove you right, your conjecture will become a theorem.

However, if you have an idea that you can demonstrate is true, or you can assume it to be demonstrable, you've got yourself a true theorem. In other words, you must provide a proof, or otherwise persuade the world that you have one.

Fermat's Last Theorem and Conjecture

This is where the confusion arrises between Fermat's Conjecture and his Last Theorem. In fact, they are the same. Because we haven't got his proof, what he stated is sometimes called 'conjecture'. However, as he was adamant that there was a proof, but he could not write it down in the margin of the Diophanti's Arithmetica, which he was reading at the time, presumably, when he produced a proof, we sometimes also call it Fermat's Last Theorem.

Fermat's Last Theorem/Fermat's Conjecture states that, although there are tripples such as a, b, c for which it is valid to state

there are no numbers x, y, and z for which

is valid, when n >= 2.

In fact, what this means is that people who believe Fermat's claim consider his statement to be his last theorem, and those who are less kind to his memory call it a conjecture.

See the next page - the page on Fermat's Last Theorem - which contains a bit more on the same subject.

Click on the picture above to find more about Fermat.

is also known as Pythagoras' Theorem. Click on the equation to learn more about it and its history.

Click on the picture below to download a presentation on Fermat's Last Theorem.