Geodesic
On a~method of solving Diophantine equations
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 189-192

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The article proposes an elementary method of finding points on elliptic curves without using algebro-geometric techniques. 
@article{ZNSL_2012_400_a8,
     author = {B. B. Lur'e},
     title = {On a~method of solving {Diophantine} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {189--192},
     publisher = {mathdoc},
     volume = {400},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a8/}
}
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B. B. Lur'e. On a~method of solving Diophantine equations. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 189-192. http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a8/