A note on the Diophantine equation |ax−by|=c
DOI:
https://doi.org/10.7146/math.scand.a-15149Abstract
Let a,b, and c be positive integers. We show that if (a,b)=(Nk−1,N), where N,k≥2, then there is at most one positive integer solution (x,y) to the exponential Diophantine equation |ax−by|=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)x−Ny|=c has more than one positive integer solutions (x,y).Downloads
Published
2010-12-01
How to Cite
He, B., Togbé, A., & Yang, S. (2010). A note on the Diophantine equation |ax−by|=c. MATHEMATICA SCANDINAVICA, 107(2), 161–173. https://doi.org/10.7146/math.scand.a-15149
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