A Non Fiction Trilogy

Appendix M Fermatâ€™s Theorem

https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem

saw this Fermatâ€™s theorem in a book so gave the solution a try

for positive
integers
a^{2} + b^{2}
cannot = c^{2}

why? take the numbers if a + b = c then obviously the squares will not equal as powering up separate #'s at separate rates, c always greater.

therefore, if c greater still will not equal, so only if c is
less than a, b might it be equal. Say if b greater than a and if c=b will not
work so only if c is between a and b. But then square root of a^{2}-b^{2}
= square root of a^{2} +
b^{2}
or

a - b = a + b which is not so. Same then for any other power/exponent (to the 3rd or 4th etc.) as is as proportional increase with new power (relative to each term), though not directly so.

But I probably am missing something. Also I saw somewhere it had been solved recently anyhow.