E. S. Ismail

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math.NT2025

Integer solutions of Pell equation in bounded regions

Kun Yi Ong, Eddie Shahril Bin Ismail

The Pell equation $x^{2} - D y^{2} = 1$ with non-square $D > 1$ has infinitely many integer solutions, yet most research has centered on the asymptotic behavior of fundamental units as…

math.NT2025

Integer roots of LA2-type function in the closed rotated square region

Ong Kun Yi, Eddie Shahril Bin Ismail

Let $A$ be the set of all Diophantine equations of the form $a u^{2} + b uv + c v^{2} + d u + e v + f = 0$ , where $a, b, c, d, e, f \in Z$ and $a > 0$ . One way to solve the eq…