A note on the diophantine equation x
2 + b
y
= c
z |
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Authors: | Maohua Le |
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Institution: | (1) Department of Mathematics, Zhanjiang Normal College, Zhanjiang, Guangdong, P. R. China |
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Abstract: | Let a, b, c, r be positive integers such that a
2 + b
2 = c
r
, min(a, b, c, r) > 1, gcd(a, b) = 1, a is even and r is odd. In this paper we prove that if b ≡ 3 (mod 4) and either b or c is an odd prime power, then the equation x
2 + b
y
= c
z
has only the positive integer solution (x, y, z) = (a, 2, r) with min(y, z) > 1. |
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Keywords: | exponential diophantine equation Lucas number positive divisor |
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