A note on the exponential Diophantine equation (4m²+1)x+(5m²-1)y=(3m)z
Jianping Wang ; Tingting Wang ; Wenpeng Zhang
Colloquium Mathematicae, Tome 139 (2015), p. 121-126 / Harvested from The Polish Digital Mathematics Library
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Let m be a positive integer. Using an upper bound for the solutions of generalized Ramanujan-Nagell equations given by Y. Bugeaud and T. N. Shorey, we prove that if 3 ∤ m, then the equation (4m²+1)x+(5m²-1)y=(3m)z has only the positive integer solution (x,y,z) = (1,1,2).

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:283767 
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     author = {Jianping Wang and Tingting Wang and Wenpeng Zhang},
     title = {A note on the exponential Diophantine equation $(4m$^2$+1)^x + (5m$^2$-1)^y = (3m)^z$
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     journal = {Colloquium Mathematicae},
     volume = {139},
     year = {2015},
     pages = {121-126},
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     language = {en},
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Jianping Wang; Tingting Wang; Wenpeng Zhang. A note on the exponential Diophantine equation $(4m²+1)^x + (5m²-1)^y = (3m)^z$
            . Colloquium Mathematicae, Tome 139 (2015) pp. 121-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-1-7/