Jerome T. Dimabayao

collaborators

3 papers

math.NT2023

Density results for the parity of $(4 k, k)$ -singular overpartitions

Victor Manuel Aricheta, Jerome Dimabayao, Hazel Joy Shi

The $(k, i)$ -singular overpartitions, combinatorial objects introduced by Andrews in 2015, are known to satisfy Ramanujan-type congruences modulo any power of prime coprime to $6 k$ .…

math.NT2023

A variant of the congruent number problem

Jerome T. Dimabayao, Soma Purkait

A positive integer $n$ is called a $θ$ -congruent number if there is a triangle with sides $a, b$ and $c$ for which the angle between $a$ and $b$ is equal to $θ$ and its area is $n\s…

math.NT2019

Je{ś}manowicz' conjecture for polynomials

Jerome T. Dimabayao

Let $(a, b, c)$ be pairwise relatively prime integers such that $a^{2} + b^{2} = c^{2}$ . In 1956, Je{ś}manowicz conjectured that the only solution of $a^{x} + b^{y} = c^{z}$ in positive integers…

Density results for the parity of (4k,k)-singular overpartitions

A variant of the congruent number problem

Je{ś}manowicz' conjecture for polynomials

Density results for the parity of $(4 k, k)$ -singular overpartitions