AbstractIterating the Euler ϕ-function, we write ϕl(n) = ϕ (ϕl − 1(n)), and, for a fixed l, we investigate the integers n which are solutions of the arithmetic equation n = kϕl(n), for some integer k
AbstractWe consider the ternary Goldbach problem with two prime variables of the form k2+m2+1 and fi...
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
We show that for some $k\le 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi(n)=...
AbstractWe study the solutions of the equation ϕ(Cm)/ϕ(Cn)=r, where r is a fixed rational number, Ck...
AbstractWe prove that the equation xn + (x + a)n = y2n + (y + b)2n with a, b odd has only finitely m...
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, ...
AbstractLet ζn denote a primitive nth root of unity, n ≥ 4. For any integer k, 2 ≤ k ≤ n − 2 it is s...
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...
AbstractLet a, b, k be non-zero integers. Then the set of pairs of exponents (m, n), m ≧ 1, n ≧ 1, f...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
In this remark, we use some properties of simple continued fractions of quadratic irrational numbers...
AbstractLet N′(k) denote the number of coprime integral solutions x, y of y2 = x3 + k. It is shown t...
AbstractWe consider the ternary Goldbach problem with two prime variables of the form k2+m2+1 and fi...
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
We show that for some $k\le 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi(n)=...
AbstractWe study the solutions of the equation ϕ(Cm)/ϕ(Cn)=r, where r is a fixed rational number, Ck...
AbstractWe prove that the equation xn + (x + a)n = y2n + (y + b)2n with a, b odd has only finitely m...
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, ...
AbstractLet ζn denote a primitive nth root of unity, n ≥ 4. For any integer k, 2 ≤ k ≤ n − 2 it is s...
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...
AbstractLet a, b, k be non-zero integers. Then the set of pairs of exponents (m, n), m ≧ 1, n ≧ 1, f...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
In this remark, we use some properties of simple continued fractions of quadratic irrational numbers...
AbstractLet N′(k) denote the number of coprime integral solutions x, y of y2 = x3 + k. It is shown t...
AbstractWe consider the ternary Goldbach problem with two prime variables of the form k2+m2+1 and fi...
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
We show that for some $k\le 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi(n)=...
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