Geodesic
Complete solutions of a Lebesgue-Ramanujan-Nagell type equation
Archivum mathematicum, Tome 60 (2024) no. 3, pp. 135-144 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider the Lebesgue-Ramanujan-Nagell type equation $x^2+5^a13^b17^c=2^m y^n$, where $a,b,c, m\ge 0, n \ge 3$ and $x, y\ge 1$ are unknown integers with $\gcd (x,y)=1$. We determine all integer solutions to the above equation. The proof depends on the classical results of Bilu, Hanrot and Voutier on primitive divisors in Lehmer sequences, and finding all $S$-integral points on a class of elliptic curves.
We consider the Lebesgue-Ramanujan-Nagell type equation $x^2+5^a13^b17^c=2^m y^n$, where $a,b,c, m\ge 0, n \ge 3$ and $x, y\ge 1$ are unknown integers with $\gcd (x,y)=1$. We determine all integer solutions to the above equation. The proof depends on the classical results of Bilu, Hanrot and Voutier on primitive divisors in Lehmer sequences, and finding all $S$-integral points on a class of elliptic curves.
DOI : 10.5817/AM2024-3-135
Classification : 11D41, 11D61, 11Y50
Keywords: Diophantine equation; Lehmer sequence; elliptic curve; quartic curve; S-integral points 
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Baruah, Priyanka; Das, Anup; Hoque, Azizul. Complete solutions of a Lebesgue-Ramanujan-Nagell type equation. Archivum mathematicum, Tome 60 (2024) no. 3, pp. 135-144. doi: 10.5817/AM2024-3-135

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