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.
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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