Fermat's Last Theorem

[TonyMcC]

This speculation has some similarities to the four colour map theorem.

 

I speculate that any calculating device, including the human brain, cannot accurately calculate integer values A,B and C for the equation A^n + B^n = C^n (except where n=1 or n=2) unless provided with three pieces of information.

 

If Fermat's last theorem is correct then he implies at least one of the given integers (A,B or C) is irrational. This leads to the thought that geometry would be the most likely means for finding a solution. (Somewhat like proofs for A^2 + B^2 = c^2). The problem here is that given A and B you cannot draw a triangle showing A, B and C unless you are provided with the included angle. This angle is different for each different pair of lines A and B and thus is a neccessary third input.

 

A very similar arguement comes from the realisation that an analogue computer fed with sine wave inputs A and B would have no difficulty providing the reqired sine wave of value C if also fed with an angle to phase shift the other two inputs before adding them together.

 

A phasor diagram could be imagined showing phasors A, B and C, but a phasor diagram only applies to sine waves. Being sine waves each component is the square root of "something". Therefore as well as the angle problem you have to be told that the diagram only applies to sine waves and each value is the square root of "something".

 

Much of this speculation appears in my thread concerning simple thoughts about Fermat's Last Theorem.