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A Diophantine equation. (English) Zbl 0576.10010
The author finds by the elementary theory of algebraic number fields all the cases when the sum of three consecutive integral cubes is a square; that is to find all integral solutions $$x,y$$ of $$y^ 2=(x-1)^ 3+x^ 3+(x+1)^ 3=3x(x^ 2+2)$$.
Editor’s remark: In an addendum in Glasg. Math. J. 29, 275 (1987; Zbl 0642.10019) priority of this result for S. Uchiyama is acknowledged.

##### MSC:
 11D25 Cubic and quartic Diophantine equations 14G20 Local ground fields in algebraic geometry 11D88 $$p$$-adic and power series fields
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##### References:
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