Sanda Bujačić | Searcharxiv

arXiv2016

A variation of a congruence of Subbarao for n=2^(alpha)*5^(beta)

There are many open problems concerning the characterization of the positive integers $n$ fulfilling certain congruences and involving the Euler totient function $φ$ and the sum of positive divisors function $σ$ of the positive integer $n$. In this work, we deal with the congruence of the form $$ nφ(n)\equiv2\pmod{σ(n)} $$ and we prove that the only positive integers of the form $2^α5^β, \enspace α, β\geq0,$ that satisfy the above congruence are $n=1, 2, 5, 8$.

math.NT↗

arXiv2014

Two divisors of (n^2+1)/2 summing up to δn+ε, for δ and ε even

In this paper we are dealing with the problem of the existence of two divisors of $(n^2+1)/2$ whose sum is equal to $δn+\varepsilon$, in the case when $δ$ and $\varepsilon$ are even, or more precisely in the case in which $δ\equiv\varepsilon+2\equiv0$ or $2 \pmod{4}$. We will completely solve the cases $δ=2, δ=4$ and $\varepsilon=0$.

math.NT↗