Some Arithmetic Properties Of Harmonic Number

We denote by the nth harmonic number.In this paper we investigate some arithmetic properties of harmonic number and obtain some results as follows:let m≥2be a positive integer,for any prime p>2m+2, we have On the other hand,we get the following result: for any prime p (?) A-4,at least one of the following two congruences holds: where A≠±4,Lucas sequence un(A)satisfies:u0(A)=0,u1(A)=1,un+2(A)=Aun+1(A)-4Un(A),n=0,1,2,...