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On the Diophantine equation $ \sum X\sb{i}=\prod X\sb{i}$

Author: M. L. Brown
Journal: Math. Comp. 42 (1984), 239-240
MSC: Primary 11D72
MathSciNet review: 726001
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Abstract: The diophantine equation $ {X_1} + \cdots + {X_k} = {X_1} \cdots {X_k}$ has at least one solution in positive integers for $ k \geqslant 2$. The set of integers k for which this is the only solution are investigated; in particular, this set is conjectured to be a known finite sequence.

References [Enhancements On Off] (What's this?)

  • [1] Richard K. Guy, Unsolved problems in number theory, Unsolved Problems in Intuitive Mathematics, vol. 1, Springer-Verlag, New York-Berlin, 1981. Problem Books in Mathematics. MR 656313
  • [2] M. Misiurewicz, "Ungelöste Probleme," Elem. Math., v. 21, 1966, p. 90.

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Keywords: Diophantine equation, prime numbers
Article copyright: © Copyright 1984 American Mathematical Society