### The Number of Irreducible Polynomials over a Finite Field : An Algebraic Proof

#### Abstract

of irreducible polynomial of degree n over Z_p is given and also proved using abstract algebra approach. Because the number is always positive, for any prime integer p and natural number n, an irreducible polynomial of degree n over Z_p always exists. Moreover, it implies that a finite field of order p^n always exists.

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