Earthline Journal of Mathematical Sciences

A Note on a Lebesgue-Ramanujan-Nagell Type Diophantine Equation

Mustafa Aydın, Murat Alan — Mon, 07 Sep 2026 00:00:00 +0000

We determine all solutions of
\[
x^2+3^a7^b37^c=\lambda y^n,
\]
where $\lambda\in\{1,2,4\}$, $x,y\geq1$, $a,b,c\geq0$, $n\geq3$, and $\gcd(x,y)=1$, subject to the following parity condition: when $\lambda\in\{1,2\}$ and neither $3$ nor $4$ divides $n$, the integer $y$ is assumed to be odd. The cases divisible by $3$ or $4$ are reduced to the determination of $S$-integral points on elliptic and quartic curves, with $S=\{3,7,37\}$. For the remaining exponents, a reduction to odd prime exponents is combined with the primitive divisor theorem for Lehmer sequences and the corrected classification of defective Lehmer pairs. All computationally obtained solutions are then checked directly in the original equation.

On an Inequality Analogous to the Nesbitt Inequality

Christophe Chesneau — Mon, 07 Sep 2026 16:16:40 +0000

In this paper, we first examine a cyclic inequality analogous to the Nesbitt inequality, and subsequently establish generalized versions using convex functions and the Jensen inequality. Several applications are provided to illustrate the main results.

Linear-Interpolative Contraction Mapping Theorem for the Berinde Weak, Kannan, Ciric-Reich-Rus, and Chatterjea Operators in Metric Spaces with Application

Clement Boateng Ampadu — Mon, 07 Sep 2026 00:00:00 +0000

Motivated by the definition of interpolative metric space [6], in which the triangle inequality has been modified into an inequality consisting of linear and interpolative terms, we introduce in this paper the notion of linear-interpolative contractions which is analogous to the triangle inequality in the definition of interpolative metric space. These inequalities consist of linear and interpolative terms. Some results related to the linear-interpolative contractions are obtained in the setting of metric spaces with an illustrative example. Finally, we apply our result to the Fredholm integral equation.