A Research on Fermat Little Theorem and Its Euler's Generalization: Selected Proofs

Exploring Proofs and Generalizations of Fermat's Little Theorem

Abstract

In this examination , we spread Fermat Little Theorem, Euler's generalization of this theorem, and. Fermat's Little Theorem, and Euler's theorem are two of the most significant theorems of present day number theory. Since it is so crucial, we set aside the effort to give two proofs of Fermat's theorem (I) the acceptance based proof, and (ii) the change based proof. The second of these sums up to give a proof of Euler's theorem. There is a third proof utilizing bunch theory, however we center around the two increasingly rudimentary proofs. We present a few ways to deal with a conceivable basic proof of Fermat's Little Theorem (FLT), which expresses that for all n more prominent than 2, there don't exist x, y, z to such an extent that xn + yn = zn, where x, y, z, n, are certain whole numbers.