A note on the ternary purely exponential diophantine equation Ax + By = Cz with A + B = C2
2020 ◽
Vol 57
(2)
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pp. 200-206
Keyword(s):
AbstractLet l,m,r be fixed positive integers such that 2| l, 3lm, l > r and 3 | r. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{rlm2 − 1,(l − r)lm2 + 1} > 30, then the equation (rlm2 − 1)x + ((l − r)lm2 + 1)y = (lm)z has only the positive integer solution (x,y,z) = (1,1,2).
2012 ◽
Vol 241-244
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pp. 2650-2653
2014 ◽
Vol 90
(1)
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pp. 1701-1708
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pp. 30-35
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Vol 90
(1)
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pp. 20-27
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Vol 14
(05)
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pp. 1223-1228
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Vol 29
(3)
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pp. 23-32