Does Fermat's Last theorem have any real life applications?

Answer 1

It's great for inspiring generations of mathematicans to study abstract algebra and number theory! And these, in turn, can have real life applications, in areas such as computer design, approximation series such as are used in engineering math, and cryptography.
Fortunately, mathematicians are happy to study such things in the abstract, without regard for whether or not they have "real life" applications. Then, later, the applied science folks find out that this stuff is useful as well as beautiful.
See for example...
http://www.mbay.net/~cgd/flt/fltmain.htm

Answer 2

Well, here's a real-life geometrical application:

Suppose you took a triangle with sides of length a, b, and c.
If I told you that the length of the sides satisfied the equality
a^3 + b^3 = c^3 (where ^3 means cubed), Fermat's theorem would say that at most only two of the sides could be of integral length (a whole number).

If all three lengths were whole numbers, then Fermat's theorem would be false.

In fact, I can replace the 3 in the equation with any positive whole number greater than 2 and draw the same conclusion.

Answer 3

cryptography rings a bell