On the Diophantine equation Σi=1k 1/Xi = 1 in distinct integers of the form xi pαqβ

Nechemia Burshtein
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 16, 2010, Number 4, Pages 1—5
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Authors and affiliations

Nechemia Burshtein
117 Arlozorov Street, Tel Aviv 62098, Israel

Abstract

A complete demonstration of solutions of the above Diophantine equation is given when p < q are primes and α, β are positive integers. Among the several examples exhibited, Example 3 provides a new solution containing eighty-five even numbers xi all of which are of the required form. Certain questions and modifications of the equation are also discussed.

Keywords

  • Diophantine equations
  • Egyptian fractions

AMS Classification

  • 11D68

References

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    http://www.primepuzzles.net/.

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Cite this paper

Burshtein, N. (2010). On the Diophantine equation Σi=1k 1/Xi = 1 in distinct integers of the form xi pαqβ. Notes on Number Theory and Discrete Mathematics, 16(4), 1-5.

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