Geodesic
On the diophantine equation $x^2+2^a3^b73^c=y^n $
Archivum mathematicum, Tome 59 (2023) no. 5, pp. 411-420
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In this paper, we find all integer solutions $ (x, y, n, a, b, c) $ of the equation in the title for non-negative integers $ a, b$ and $ c $ under the condition that the integers $ x $ and $ y $ are relatively prime and $ n \ge 3$. The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.
In this paper, we find all integer solutions $ (x, y, n, a, b, c) $ of the equation in the title for non-negative integers $ a, b$ and $ c $ under the condition that the integers $ x $ and $ y $ are relatively prime and $ n \ge 3$. The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.
DOI : 10.5817/AM2023-5-411
Classification : 11D59, 11D61, 11Y50
Keywords: diophantine equations; primitive divisor theorem; Ramanujan-Nagell equations 
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Alan, Murat; Aydin, Mustafa. On the diophantine equation $x^2+2^a3^b73^c=y^n $. Archivum mathematicum, Tome 59 (2023) no. 5, pp. 411-420. doi: 10.5817/AM2023-5-411

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