Fermat's Last Theorem on Facebook

Fermat's Last Theorem (FLT) is perhaps the most famous mathematical puzzle of all time. It was formulated as a conjecture by Pierre de Fermat in 1637 and was only proven in 1995 by Andrew Wiles.


FLT states that no three positive integers a, b, and c can satisfy the equation 

aⁿ + bⁿ = cⁿ   [1]

for any integer value of n greater than 2.

A very interesting fact about FLT is how Fermat introduced it to the world. He wrote the following on the margin of the book Arithmetica:

I have discovered a truly marvelous proof that 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. This margin is too narrow to contain it.

With this seemingly casual and yet bold statement, Fermat issued a challenge to the great mathematical minds of his time (which included Blaise Pascal) and of the three centuries that follow.

If Fermat lived in this Facebook generation, I think he could have introduced this theorem in the following way:

[1] Note that if n=2, the formula above becomes a² + b² = c². Because of our familiarity and use of the Pythagorean Theorem, we know that there are positive integers a, b and c that satisfy this equation. Two examples are 3,4,5 and 6,8,10. Fermat's Last Theorem states that no such triples could be found for n greater than 2.


[2] Click here for an article on Faith, Reason and Fermat's Last Theorem

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