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Sunday, January 6, 2008

Fermat last theorem

Prove Fermat's Last theorem for n=3 : X^3 + Y^3 = Z^3 where X, Y, Z are rational integers, then X, Y, or Z is 0.
This is interesting one.Here`s something about Fermat from wiki:
is the name of the statement in number theory that:

It is impossible to separate any power higher than the second into two like powers,

or, more precisely:

If an integer n is greater than 2, then the equation an + bn = cn has no solutions in non-zero integers a, b, and c.

In 1637 Pierre de Fermat wrote, in his copy of Claude-Gaspar Bachet`s translation of the famous Arithmetica of Diophantus, "I have a truly marvelous proof of this proposition which this margin is too narrow to contain." (Original Latin: "Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.")

Fermat's Last Theorem is strikingly different and much more difficult to prove than the analogous problem for n = 2, for which there are infinitely many integer solutions called Pythagorean triples (and the closely related Pythagorean theorem has many elementary proofs). The fact that the problem's statement is understandable by schoolchildren makes it all the more frustrating, and it has probably generated more incorrect proofs than any other problem in the history of mathematics. No correct proof was found for 357 years, when a proof was finally published by Andrew Wiles in 1995. The term "last theorem" resulted because all the other theorems proposed by Fermat were eventually proved or disproved, either by his own proofs or by other mathematicians, in the two centuries following their proposition. Although a theorem now that it has been proved, the status of Fermat's Last Theorem before then, in spite of the name, was that of a conjecture, a mathematical statement whose status (true or false) has not been conclusively settled.

Fermat's Last Theorem is the most famous solved problem in the history of mathematics , familiar to all mathematicians, and had achieved a recognizable status in popular culture prior to its proof.

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