Paulius Virbalas

collaborators

3 papers

math.NT2026

On the generalized Sierpiński and Riesel numbers

Paulius Virbalas

In this paper, we prove that for any fixed base $b \geq 2$ , there exists an infinite arithmetic progression of positive integers $k$ that are simultaneously generalized Sierpiński a…

math.NT2026

On the exponential Diophantine equation $(a^{n} + 1) (b^{n} + 1) = x^{2}$

Paulius Virbalas

We study the Diophantine equation $(a^{n} + 1) (b^{n} + 1) = x^{2}$ , which belongs to the family of equations originating from the work of Szalay in 2000. If $a > 1$ , it is shown that the equatio…

math.NT2026

Perfect powers among Jacobsthal numbers

Paulius Virbalas

Jacobsthal numbers are an example of a Lucas sequence defined by a recurrence relation analogous to that of the Fibonacci numbers, but with different parameters. In this paper, we…

On the generalized Sierpiński and Riesel numbers

On the exponential Diophantine equation (an+1)(bn+1)=x2

Perfect powers among Jacobsthal numbers

On the exponential Diophantine equation $(a^{n} + 1) (b^{n} + 1) = x^{2}$