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In this article, we discuss whether a single congruent number $t$ can have two (or more) distinct triangles with the same hypotenuse. We also describe and carry out computational experimentation providing evidence that this does not occur.
We introduce a shifted convolution sum that is parametrized by the squarefree natural number $t$. The asymptotic growth of this series depends explicitly on whether or not $t$ is a emph{congruent number}, an integer that is the area of a rational rig
We take an approach toward counting the number of n for which the curves E_n: y^2=x^3-n^2x have 2-Selmer groups of a given size. This question was also discussed in a pair of Invent. Math. papers by Roger Heath-Brown. We discuss the connection betwee
In this paper, $p$ and $q$ are two different odd primes. First, We construct the congruent elliptic curves corresponding to $p$, $2p$, $pq$, and $2pq,$ then, in the cases of congruent numbers, we determine the rank of the corresponding congruent elliptic curves.
Let $mathbb{F}_q$ be a finite field of odd characteristic. We study Redei functions that induce permutations over $mathbb{P}^1(mathbb{F}_q)$ whose cycle decomposition contains only cycles of length $1$ and $j$, for an integer $jgeq 2$. When $j$ is $4
We study a curious class of partitions, the parts of which obey an exceedingly strict congruence condition we refer to as sequential congruence: the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part congruent to zero mo