# Applications of Fermat’s Little Theorem

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## Abstract

Fermat’s Little Theorem that is used to simplify the progression of converting a power of a number to a prime modulus is known as the most crucial theorem in elementary number theory. The credit of this theorem goes to Pierre de Fermat. This theorem is an exclusive situation of Euler’s theorem and is pretty helpful in application of number theory such as congruence relation modulo *n* and public-key cryptography. Compared to Fermat’s Last theorem which notes that when , has no solutions .(Riehm & Dudley), Fermat’s this theorem is titled as “little”. Fermat’s Last Theorem remained unsolved for several years in the field of mathematics. Fermat described this theorem some 350 years ago and Andrew Wiles proved it in 1995. It is simple to prove Fermat’s Little Theorem, but it has a wide implication for cryptography.