Learn More
In this work, we state and prove Lerch's theorems for Fermat and Euler quotients over function fields defined analogously to the number fields. The Fermat's little theorem states that if p is a prime and a is an integer not divisible by p, then a p−1 ≡ 1 mod p. This gives rise to the definition of the Fermat quotient of p with base a, q(a, p) = a p−1 − 1 p(More)
In this work, we study the elliptic curve E : y 2 = f (x), where f (x) is a cubic permutation polynomial over some finite commutative ring R. In case R is the finite field F q , it turns out that the group of rational points on E is cyclic of order q + 1. This group is a product of cyclic groups if R = Z n , the ring of integers modulo a square-free n. In(More)
In this work, we study several equivalence relations induced from the partitions of the sets of words of finite length. We have results on words over finite fieldsties of its equivalence classes and explicit relationships between two words are determined. Moreover, we deal with words of finite length over the ring Z/N Z where N is a positive integer. We(More)