ON THE DIOPHANTINE EQUATION x2 + C = 2yn
2009 ◽
Vol 05
(06)
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pp. 1117-1128
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Keyword(s):
In this paper, we study the Diophantine equation x2 + C = 2yn in positive integers x,y with gcd (x,y) = 1, where n ≥ 3 and C is a positive integer. If C ≡ 1 (mod 4), we give a very sharp bound for prime values of the exponent n; our main tool here is the result on existence of primitive divisors in Lehmer sequences due to Bilu, Hanrot and Voutier. We illustrate our approach by solving completely the equations x2 + 17a1 = 2yn, x2 + 5a113a2 = 2yn and x2 + 3a111a2 = 2yn.
2020 ◽
Vol 57
(2)
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pp. 200-206
2013 ◽
Vol 89
(2)
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pp. 316-321
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2010 ◽
Vol 81
(2)
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pp. 177-185
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Keyword(s):
2012 ◽
Vol 08
(03)
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pp. 813-821
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2014 ◽
Vol 90
(1)
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pp. 9-19
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2013 ◽
Vol 94
(1)
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pp. 50-105
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2006 ◽
Vol 02
(02)
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pp. 195-206
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Keyword(s):
2016 ◽
Vol 95
(1)
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pp. 5-13
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