A note on the Diophantine equation |axby|=c

Authors

  • Bo He
  • Alain Togbé
  • Shichun Yang

DOI:

https://doi.org/10.7146/math.scand.a-15149

Abstract

Let a,b, and c be positive integers. We show that if (a,b)=(Nk1,N), where N,k2, then there is at most one positive integer solution (x,y) to the exponential Diophantine equation |axby|=c, unless (N,k)=(2,2). Combining this with results of Bennett [3] and the first author [6], we stated all cases for which the equation |(Nk±1)xNy|=c has more than one positive integer solutions (x,y).

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Published

2010-12-01

How to Cite

He, B., Togbé, A., & Yang, S. (2010). A note on the Diophantine equation |axby|=c. MATHEMATICA SCANDINAVICA, 107(2), 161–173. https://doi.org/10.7146/math.scand.a-15149

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Articles