On the Diophantine equation x
2+5
m
=y
n |
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| Authors: | Liqun Tao |
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| Institution: | (1) Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China;(2) School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland |
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| Abstract: | In this paper we consider the Diophantine equation x
2+5
m
=y
n
, n>2, m>0. We prove that the equation has no positive integer solutions when 2∤
m, nor when 2∣m under the additional condition (x,y)=1, with the help of Bilu, Hanrot, and Voutier’s deep result in (J. Reine Angew. Math. 539:75–122, 2001).
Supported by the 973 Grant of P.R.C and SRFDP 20040284018. |
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| Keywords: | Diophantine equation Quadratic field |
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