Matches in SemOpenAlex for { <https://semopenalex.org/work/W3035676841> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W3035676841 abstract "A positive integer that is the area of some rational right triangle is called a congruent number. In an algebraic point of view, being a congruent number means satisfying a system of equations. As early as the 1800s, it is understood that if $n$ is a congruent number, then the equation $nm^2 = uv(u^2 - v^2)$ has a solution in $mathbb{Z}$. Using the relation between congruent numbers and elliptic curves $E_n: y^2 = x^3 - n^2 x$ which was established in the 1900s, we will prove that the converse of this two century-old result holds as well. In addition to this, we present another proof of the converse using the method of 2-descent. Towards the end of this paper, we demonstrate how one can use our proof to construct subfamilies of $E_n$ with rank at least 2 and 3." @default.
- W3035676841 created "2020-06-19" @default.
- W3035676841 creator A5032067620 @default.
- W3035676841 date "2020-06-15" @default.
- W3035676841 modified "2023-09-27" @default.
- W3035676841 title "Constructing congruent number elliptic curves using 2-descent" @default.
- W3035676841 cites W2000376595 @default.
- W3035676841 cites W2024074281 @default.
- W3035676841 cites W2039187350 @default.
- W3035676841 cites W2039798834 @default.
- W3035676841 hasPublicationYear "2020" @default.
- W3035676841 type Work @default.
- W3035676841 sameAs 3035676841 @default.
- W3035676841 citedByCount "0" @default.
- W3035676841 crossrefType "posted-content" @default.
- W3035676841 hasAuthorship W3035676841A5032067620 @default.
- W3035676841 hasConcept C114614502 @default.
- W3035676841 hasConcept C118615104 @default.
- W3035676841 hasConcept C121332964 @default.
- W3035676841 hasConcept C134306372 @default.
- W3035676841 hasConcept C153294291 @default.
- W3035676841 hasConcept C164226766 @default.
- W3035676841 hasConcept C179603306 @default.
- W3035676841 hasConcept C199360897 @default.
- W3035676841 hasConcept C202444582 @default.
- W3035676841 hasConcept C2524010 @default.
- W3035676841 hasConcept C2776637919 @default.
- W3035676841 hasConcept C2776809875 @default.
- W3035676841 hasConcept C33923547 @default.
- W3035676841 hasConcept C41008148 @default.
- W3035676841 hasConcept C9376300 @default.
- W3035676841 hasConcept C97137487 @default.
- W3035676841 hasConceptScore W3035676841C114614502 @default.
- W3035676841 hasConceptScore W3035676841C118615104 @default.
- W3035676841 hasConceptScore W3035676841C121332964 @default.
- W3035676841 hasConceptScore W3035676841C134306372 @default.
- W3035676841 hasConceptScore W3035676841C153294291 @default.
- W3035676841 hasConceptScore W3035676841C164226766 @default.
- W3035676841 hasConceptScore W3035676841C179603306 @default.
- W3035676841 hasConceptScore W3035676841C199360897 @default.
- W3035676841 hasConceptScore W3035676841C202444582 @default.
- W3035676841 hasConceptScore W3035676841C2524010 @default.
- W3035676841 hasConceptScore W3035676841C2776637919 @default.
- W3035676841 hasConceptScore W3035676841C2776809875 @default.
- W3035676841 hasConceptScore W3035676841C33923547 @default.
- W3035676841 hasConceptScore W3035676841C41008148 @default.
- W3035676841 hasConceptScore W3035676841C9376300 @default.
- W3035676841 hasConceptScore W3035676841C97137487 @default.
- W3035676841 hasLocation W30356768411 @default.
- W3035676841 hasOpenAccess W3035676841 @default.
- W3035676841 hasPrimaryLocation W30356768411 @default.
- W3035676841 hasRelatedWork W1516953373 @default.
- W3035676841 hasRelatedWork W1901474581 @default.
- W3035676841 hasRelatedWork W2067569566 @default.
- W3035676841 hasRelatedWork W2073825288 @default.
- W3035676841 hasRelatedWork W2097274343 @default.
- W3035676841 hasRelatedWork W2136231133 @default.
- W3035676841 hasRelatedWork W2237086442 @default.
- W3035676841 hasRelatedWork W2298326006 @default.
- W3035676841 hasRelatedWork W2556214087 @default.
- W3035676841 hasRelatedWork W2784021273 @default.
- W3035676841 hasRelatedWork W2796068151 @default.
- W3035676841 hasRelatedWork W2893336498 @default.
- W3035676841 hasRelatedWork W2950662621 @default.
- W3035676841 hasRelatedWork W2963356545 @default.
- W3035676841 hasRelatedWork W2964204138 @default.
- W3035676841 hasRelatedWork W3012561618 @default.
- W3035676841 hasRelatedWork W3089561538 @default.
- W3035676841 hasRelatedWork W3163994581 @default.
- W3035676841 hasRelatedWork W3209625879 @default.
- W3035676841 hasRelatedWork W84312700 @default.
- W3035676841 isParatext "false" @default.
- W3035676841 isRetracted "false" @default.
- W3035676841 magId "3035676841" @default.
- W3035676841 workType "article" @default.