AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n) = m + ν(m) has many solutions with n ≠ m. We also show that if ν is replaced by an arbitrary, integer-valued function f with certain properties assumed about its average order, then the equation n + f(n) = m + f(m) has infinitely many solutions with n ≠ m
In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are...
Let s be a positive integer, p be an odd prime, q=ps, and let Fq be a finite field of q elements. Le...
We define that prime equations 1 1 1 ( , ,), , ( ,)n k nf P P f P PL L L （5） are polynomial...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
ABSTRACT. We show that the equation φ(a) = σ(b) has infinitely many solutions, where φ is Euler’s t...
2)2()1() ( =+=+ = xdxdxd infinitely-often. （1） where)(xd represents the number of distinct prime fac...
Abstract. Let!.n / denote the number of prime divisors of n and let˜.n / denote the number of prime ...
Abstract. For each of the functions f ∈ {ϕ, σ, ω, τ} and every natural number K, we show that there ...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
Abstract. We study the number and nature of solutions of the equation (n) = (n + k), where denotes ...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
RésuméThis paper is concerned with the quantityN(x,m), the number of positive integersn, 1⩽n⩽x, for ...
For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum func...
For any positive integer n, let S(n) and Z(n) denote the Smarandache function and the pseudo Smarand...
Abstract For any positive integer n, we call an arithmetical function f(n) as the F.Smarandache mult...
In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are...
Let s be a positive integer, p be an odd prime, q=ps, and let Fq be a finite field of q elements. Le...
We define that prime equations 1 1 1 ( , ,), , ( ,)n k nf P P f P PL L L （5） are polynomial...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
ABSTRACT. We show that the equation φ(a) = σ(b) has infinitely many solutions, where φ is Euler’s t...
2)2()1() ( =+=+ = xdxdxd infinitely-often. （1） where)(xd represents the number of distinct prime fac...
Abstract. Let!.n / denote the number of prime divisors of n and let˜.n / denote the number of prime ...
Abstract. For each of the functions f ∈ {ϕ, σ, ω, τ} and every natural number K, we show that there ...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
Abstract. We study the number and nature of solutions of the equation (n) = (n + k), where denotes ...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
RésuméThis paper is concerned with the quantityN(x,m), the number of positive integersn, 1⩽n⩽x, for ...
For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum func...
For any positive integer n, let S(n) and Z(n) denote the Smarandache function and the pseudo Smarand...
Abstract For any positive integer n, we call an arithmetical function f(n) as the F.Smarandache mult...
In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are...
Let s be a positive integer, p be an odd prime, q=ps, and let Fq be a finite field of q elements. Le...
We define that prime equations 1 1 1 ( , ,), , ( ,)n k nf P P f P PL L L （5） are polynomial...
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