Benjamin Earp-Lynch

most citedOn certain

D (9)

and

D (64)

Diophantine triples

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math.NT2026

Powers as Fibonacci Sums

Benjamin Earp-Lynch, Simon Earp-Lynch, Omar Kihel +1

We examine the equation $y^{a} = i = 1 \sum k F_{n_{i}}$ for positive integers $y, a \geq 2$ and $k \geq 3$ . This equation can be expressed as a problem in terms of the Zeckendor…

math.NT2026★ 1 cited

On certain $D (9)$ and $D (64)$ Diophantine triples

Benjamin Earp-Lynch, Simon Earp-Lynch, Omar Kihel

A set of $m$ distinct positive integers ${a_{1}, \dots a_{m}}$ is called a $D (q)$ - $m$ -tuple for nonzero integer $q$ if the product of any two increased by $q$ , $a_{i} a_{j} + q$ , $i\…

math.NT2026

Extension of the Equation $j = 1 \sum k j F_{j}^{p} = F_{n}^{q}$ to a Family of Lucas Sequences

Benjamin Earp-Lynch, Simon Earp-Lynch, Omar Kihel +1

We solve the equation $j = 1 \sum k j U_{j} (x, y)^{p} = U_{n} (x, y)^{q}$ positive integers $x, p, q, k, n$ , with $y = \pm 1$ and $max {p, q} \leq 11$ , where $U_{m}(x,y)=\frac{α^{m}-β^{m…

math.NT2026

Mordell Curves with Ordinates in Arithmetic Progression

Sakha A. Alkabouss, Benjamin Earp-Lynch, Simon Earp-Lynch +1

We show that Mordell curves with arithmetic progressions in the $y$ -coordinate of length $7$ have not been ruled out by previous work, and we give non-isomorphic families of Mordel…

math.NT2023

On a simple quartic family of Thue equations over imaginary quadratic number fields

Benjamin Earp-Lynch, Bernadette Faye, Eva G. Goedhart +2

Let $t$ be any imaginary quadratic integer with $∣ t ∣ \geq 100$ . We prove that the inequality \[ |F_t(X,Y)| = | X^4 - t X^3 Y - 6 X^2 Y^2 + t X Y^3 + Y^4 | \leq 1 \] has only trivial…

Powers as Fibonacci Sums

On certain D(9) and D(64) Diophantine triples

Extension of the Equation j=1∑k​jFjp​=Fnq​ to a Family of Lucas Sequences

Mordell Curves with Ordinates in Arithmetic Progression

On a simple quartic family of Thue equations over imaginary quadratic number fields

On certain $D (9)$ and $D (64)$ Diophantine triples

Extension of the Equation $j = 1 \sum k j F_{j}^{p} = F_{n}^{q}$ to a Family of Lucas Sequences