Shamik Das

collaborators

3 papers

math.NT2026

Some Remarks on $I ¨ $ -Congruent Numbers

Shamik Das, Debajyoti De

In this paper, we extend the work of \cite{Chahal} in several directions. We first determine all Heron triangles that tightly circumscribe the unit circle and the associated $I ¨ $ -c…

math.NT2026

Monsky Matrix and 2-Selmer rank

Shamik Das, Sudipa Mondal

In this article, we produce infinite families of non-congruent numbers in the residue class of $1, 2,$ and $3$ modulo $8$ with arbitrarily many triples or quadruples prime factors.…

math.NT2026

$2$ -Selmer groups, $2$ -class groups, and congruent numbers

Shamik Das, Debajyoti De, Sudipa Mondal

In this article, we study necessary conditions for certain square-free integers to be congruent numbers. Our method uses divisibility properties of class numbers of related imagina…

Some Remarks on I¨-Congruent Numbers

Monsky Matrix and 2-Selmer rank

2-Selmer groups, 2-class groups, and congruent numbers

Some Remarks on $I ¨ $ -Congruent Numbers

$2$ -Selmer groups, $2$ -class groups, and congruent numbers