saw this Fermat’s theorem in a book so gave the solution a try
for positive integers a2 + b2 cannot = c2
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 a2-b2 = square root of a2 + b2 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.