Nonetheless, mathematicians and geometrists accept that numerical expression as being equivalent. Perfect right triangles represent exact equivalencies expressed in whole numbers. This same combination of numbers in whole number terms would have to occur at powers greater than 2 in order to obtain relation of equivalency that would involve whole numbers only. The appearance of a fractional number in any one of the numbers would impede such an appearance. Nonetheless, for computational needs, this relations of equivalency is perfectly acceptable, just as any fractional expression of the Pythagorean Theorem is considered to be equivalent.
Fractional expressions constitute acceptable relations of equivalency for any power.
All other combinations of fractions or fractions and whole numbers together occur at any power. The particular conditions imposed by Fermat, that this equation represent only whole numbers for powers greater than 2 deny the possibility of achieving a relation of equivalency given the procedure of the addition of two of the terms. This may also explain one of the reasons why ancient mathematicians and geometrists preferred whole numbers. Copyrighted by Charles William Johnson. All rights reserved.