nth root theorem

In 1637, Pierre de Fermat stated in the margin of Diophantine’s Arithmetica, next to a discussion of Pythagorean triples, “It is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as the sum of two fourth powers or, in general, for any number which is a power greater than the second to be written as a sum of two like powers.”

In the year 2021 the article ‘Fermat’s last theorem: using simple arithmetic operation and the principle of digit sum number theorem’ introduce two different mathematical methods that contradict the statement made by Pierre de Fermat. Firstly, method of using simple arithmetic operation which is also called nth root theorem and the second method was using digit sum number theorem. The nth root theorem which contradict the Fermat’s Statement says that “No positive integer x, y and z forming a right angle triangle can satisfy the Pythagoreans equation if the power n >2; rather as the power n increases, the side x → 0, while the side z → y, and as the power n decreases, the side y → 0, while the side z → x” i.e. at a specific power n or -n using nth root theorem, the two sides of the equality sign are equal. And this method might be useful in the explanation of wave-particle paradox.

For more…https://www.researchgate.net/publication/358397176_nth_root_theorem