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On ax-by=c
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Aaron Hersehefield has recently proved the very interesting result that
2x-3y=c (1)
has got at most one solution when c is large. Further, by applying the following theorem of Siegel, namely,
axn-byn=k (fixed n ≥ 3)
has at most one solution if |ab| is sufficiently large, he proves that
ax-by=c (2)
has at most 9 solutions.
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