Math Camp

I remember when I was in my 10+2 days it was rumoured that a student from a local school had proved Fermat's theorem. It is years later that I am reading about the theorem. The curiosity was immense in those days. Sometimes I miss those days when we used to be obsessed with Science and Math questions. I read a bit from the book Snapshots from Hell, which is a nice book talking about fun in Mathematics.

Something about Fermat's last theorem:
X^n+Y^n=Z^n is a diophantine equation, which has no nontrivial solutions for n>2 and x.y, z being non-zero. It has a long and fascinating history and is known as Fermat's last theorem.

Fermat first scribbled Fermat's last theorem in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The scribbled note was discovered posthumously, and the original is now lost. However, a copy was preserved in a book published by Fermat's son.

The full text of Fermat's statement, written in Latin, reads "Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet" (Nagell 1951, p. 252). In translation, "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."

As a result of Fermat's marginal note, the proposition that the Diophantine equation
X^n+Y^n=Z^n
where x, y, z, and n are integers, has no nonzero solutions for n>2 has come to be known as Fermat's Last Theorem. It was called a "theorem" on the strength of Fermat's statement, despite the fact that no other mathematician was able to prove it for hundreds of years.

The restriction for n>2 is so because we have infinite value of Pythagorean triples satisfying the equation for x^2+y^2=z^2.