AbstractWe obtain an asymptotic formula for the number of square-free values among p−1, for primes p⩽x, and we apply it to derive the following asymptotic formula for L(x), the number of square-free values of the Carmichael function λ(n) for 1⩽n⩽x,L(x)=(κ+o(1))xln1−αx,where α=0.37395… is the Artin constant, and κ=0.80328… is another absolute constant
AbstractLet pm be any prime power and Kn(a,pm) be the Kloosterman sum Kn(a,pm)=∑x1=1pm⋯∑xn=1pmepm(x1...
AbstractIn this paper, we solve a family of Diophantine equations associated with families of number...
AbstractThe main purpose of this paper is to study the asymptotic property of the fourth power mean ...
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers wi...
AbstractIn this paper, we consider the generalized Catalan numbers F(s,n)=1(s−1)n+1(snn), which we c...
AbstractLet k be the power series field over a finite field of characteristic p>0. Let L be a cyclic...
AbstractWe give a family of cyclic cubic polynomials whose roots are systems of fundamental units of...
AbstractAn RSA modulus is a product M=pl of two primes p and l. We show that for almost all RSA modu...
AbstractLet q be an odd positive integer and let a be an integer coprime to q. For each integer b co...
AbstractLet Bq(r)=Kr+qK1 be the graph consisting of q distinct (r+1)-cliques sharing a common r-cliq...
Let (n) denote the number of divisors of a positive integer n, and let (n) is th...
AbstractLet p1,p2,… be the sequence of all primes in ascending order. The following result is proved...
AbstractLet rk(n) denote the number of representations of an integer n as a sum of k squares. We pro...
AbstractAndrews has established a refinement of the generating function for partitions π according t...
AbstractWhereas exponential equations have been widely studied, we will deal with integer arguments ...
AbstractLet pm be any prime power and Kn(a,pm) be the Kloosterman sum Kn(a,pm)=∑x1=1pm⋯∑xn=1pmepm(x1...
AbstractIn this paper, we solve a family of Diophantine equations associated with families of number...
AbstractThe main purpose of this paper is to study the asymptotic property of the fourth power mean ...
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers wi...
AbstractIn this paper, we consider the generalized Catalan numbers F(s,n)=1(s−1)n+1(snn), which we c...
AbstractLet k be the power series field over a finite field of characteristic p>0. Let L be a cyclic...
AbstractWe give a family of cyclic cubic polynomials whose roots are systems of fundamental units of...
AbstractAn RSA modulus is a product M=pl of two primes p and l. We show that for almost all RSA modu...
AbstractLet q be an odd positive integer and let a be an integer coprime to q. For each integer b co...
AbstractLet Bq(r)=Kr+qK1 be the graph consisting of q distinct (r+1)-cliques sharing a common r-cliq...
Let (n) denote the number of divisors of a positive integer n, and let (n) is th...
AbstractLet p1,p2,… be the sequence of all primes in ascending order. The following result is proved...
AbstractLet rk(n) denote the number of representations of an integer n as a sum of k squares. We pro...
AbstractAndrews has established a refinement of the generating function for partitions π according t...
AbstractWhereas exponential equations have been widely studied, we will deal with integer arguments ...
AbstractLet pm be any prime power and Kn(a,pm) be the Kloosterman sum Kn(a,pm)=∑x1=1pm⋯∑xn=1pmepm(x1...
AbstractIn this paper, we solve a family of Diophantine equations associated with families of number...
AbstractThe main purpose of this paper is to study the asymptotic property of the fourth power mean ...
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