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Remark on a conjecture of Erdős on binomial coefficients


Author: Andrzej Makowski
Journal: Math. Comp. 24 (1970), 705
MSC: Primary 10.10
DOI: https://doi.org/10.1090/S0025-5718-1970-0280437-3
MathSciNet review: 0280437
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Abstract | References | Similar Articles | Additional Information

Abstract: A conjecture attributed to Erdös concerning the Diophantine equation

$\displaystyle 2\left( {\begin{array}{*{20}{c}} {x + n - 1} \\ n \\ \end{array} ... ...ht) = \left( {\begin{array}{*{20}{c}} {y + n - 1} \\ n \\ \end{array} } \right)$

is shown to be false.

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

  • [1] L. E. Dickson, History of the Theory of Numbers. Vol. II, reprint, Chelsea, New York, 1952.
  • [2] M. Wunderlich, "Certain properties of pyramidal and figurate numbers," Math. Comp., v. 16, 1962, pp. 482-486. MR 26 #6115. MR 0148608 (26:6115)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0280437-3
Keywords: Diophantine equation
Article copyright: © Copyright 1970 American Mathematical Society

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