Pierre de Fermat and his last theorem

born on August 17, 1601. In Beaumont-de-lomagne, France. He was a jurist and a great fan of mathematics, and it was this hobby that led him to do wonderful things in this field.

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Throughout history, many mathematicians such as fermat have discovered interesting properties that the numbers have, for instance the numbers 3, 4 and 5 have this particular characteristic: 3^2+4^2=5^2, and these are not the only numbers that have this feature, such is the case of 5, 12, 13 and 8, 15, 17. It is proven that there is an infinity of whole numbers that fulfill this (the Pythagorean triples).

we see then, that this property is fulfilled with powers equal to 2, but being something so simple and natural the mathematicians have wondered if this property could be generalized, they started wondering if there are three intergers X, Y and Z such that X^3+Y^3=Z^3, they could not find those numbers that satisfy this property, they also tried the case of power equal to 4 and they obtained the same results.

when they trying to generalize this property to the maximum, the mathematicians could not find three intergers (X, Y and Z) and a interger (n) bigger than 2 such that X^n+Y^n=Z^ n.

it was then Pierre de Fermat the first who affirmed that there is no integer (n) that fulfills this property, the demonstration for the case n=3 he succeeded, and wrote it on a page of a classic text of number theory the controversy begins when he try to prove the case in which n can be any number. in this case fermat affirmed the following:

It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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Fermat died on January 12, 1665. And he did not publish the proof of his theorem, the demonstration of the Fermat last theorem it was a problem that was solved 358 years later, by the mathematician Andrew Wiles, leaning on knowledge that they did not have in the time of fermat.

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