AbstractWe study the solutions of the equation ϕ(Cm)/ϕ(Cn)=r, where r is a fixed rational number, Ck is the kth Catalan number and ϕ is the Euler function. We note that the number r=4 is special for this problem and for it we construct solutions (m,n) to the above equation which are related to primes p such that 2p−1 or 4p−3 is also prime
summary:For a positive integer $n$ we write $\phi (n)$ for the Euler function of $n$. In this note, ...
Euler\u27s φ (phi) Function counts the number of positive integers not exceeding n and relatively pr...
This is a preprint of an article published in Monatshefte für Mathematik (2005), Volume 146, Number ...
Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r, where r is a fixed rational numbe...
Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r, where r is a fixed rational numbe...
AbstractWe study the solutions of the equation ϕ(Cm)/ϕ(Cn)=r, where r is a fixed rational number, Ck...
AbstractIterating the Euler ϕ-function, we write ϕl(n) = ϕ (ϕl − 1(n)), and, for a fixed l, we inves...
We study the solutions of the equation 0(Cm)/0(Cmn) = r, where r is a fixed rational number, Ck is t...
We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the ...
We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the ...
In this paper, by studying three $q$-Catalan identities given by Andrews, we arrive at a certain...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
AbstractBy using the Newton interpolation formula, we generalize the recent identities on the Catala...
summary:For a positive integer $n$ we write $\phi (n)$ for the Euler function of $n$. In this note, ...
summary:For a positive integer $n$ we write $\phi (n)$ for the Euler function of $n$. In this note, ...
Euler\u27s φ (phi) Function counts the number of positive integers not exceeding n and relatively pr...
This is a preprint of an article published in Monatshefte für Mathematik (2005), Volume 146, Number ...
Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r, where r is a fixed rational numbe...
Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r, where r is a fixed rational numbe...
AbstractWe study the solutions of the equation ϕ(Cm)/ϕ(Cn)=r, where r is a fixed rational number, Ck...
AbstractIterating the Euler ϕ-function, we write ϕl(n) = ϕ (ϕl − 1(n)), and, for a fixed l, we inves...
We study the solutions of the equation 0(Cm)/0(Cmn) = r, where r is a fixed rational number, Ck is t...
We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the ...
We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the ...
In this paper, by studying three $q$-Catalan identities given by Andrews, we arrive at a certain...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
AbstractBy using the Newton interpolation formula, we generalize the recent identities on the Catala...
summary:For a positive integer $n$ we write $\phi (n)$ for the Euler function of $n$. In this note, ...
summary:For a positive integer $n$ we write $\phi (n)$ for the Euler function of $n$. In this note, ...
Euler\u27s φ (phi) Function counts the number of positive integers not exceeding n and relatively pr...
This is a preprint of an article published in Monatshefte für Mathematik (2005), Volume 146, Number ...
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