Geodesic
ON A DIOPHANTINE EQUATION OF CASSELS
Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 303-307

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DOI

J.W.S. Cassels gave a solution to the problem of determining all instances of the sum of three consecutive cubes being a square. This amounts to finding all integer solutions to the Diophantine equation $y^2=3x(x^2+2)$. We describe an alternative approach to solving not only this equation, but any equation of the type $y^2=nx(x^2+2)$, with $n$ a natural number. Moreover, we provide an explicit upper bound for the number of solutions of such Diophantine equations. The method we present uses the ingenious work of Wilhelm Ljunggren, and a recent improvement by the authors.
DOI : 10.1017/S001708950500251X
Mots-clés : 11D25 
LUCA, F.; WALSH, P. G. ON A DIOPHANTINE EQUATION OF CASSELS. Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 303-307. doi: 10.1017/S001708950500251X
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     title = {ON {A} {DIOPHANTINE} {EQUATION} {OF} {CASSELS}},
     journal = {Glasgow mathematical journal},
     pages = {303--307},
     year = {2005},
     volume = {47},
     number = {2},
     doi = {10.1017/S001708950500251X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950500251X/}
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