Oh wow! I wouldn't have expected this so many years later. Mordel's conjecture implies asva special case that for all n>=4 there are only a finite number of solutions to Fermat's equations with relative prime numbers. Brings me back!

A point is that which has no breadth.

The line is a breadthless legth.

Mordell conjecture is that only circles or figure contain infinite points, whereas curves with exponents over 3 are finite accumulations.

"He proved that if a curve’s equation has a variable raised to a power higher than 3, then it must have a finite number of [rational] points."