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Abstract
In pure mathematics number theory is very important subject . In number theory, we study about numbers and very special properties of these numbers and group theory is also very important part of pure mathematics in group theory we study about properties of groups. In this paper we define a special relation between recurrence sequence and property of group. In number theory there are many special type of recurrence relation sequence which are depend on given initial terms and recurrence relations . A recurrence relation is important topic of mathematics. Recurrence relations are used in mathematics as well as economics,physics and others subjects. My main area of research is Number Theory. Number Theory also known as Higher Arithmetic. Thinking of famous mathematician Carl Friedrich Gauss (1777– 1855) about number theory: “Mathematics is the queen of all sciences, and Number Theory is the queen of Mathematics.” Number theory or higher arithmetic is the study of those properties of integers and rational numbers, which go beyond the ordinary manipulations of everyday arithmetic.