Differences between perfect powers: prime power gaps
MA Bennett, S Siksek - Algebra & Number Theory, 2023 - msp.org
We develop machinery to explicitly determine, in many instances, when the difference x 2−
yn is divisible only by powers of a given fixed prime. This combines a wide variety of …
yn is divisible only by powers of a given fixed prime. This combines a wide variety of …
Differences between perfect powers: The Lebesgue-Nagell equation
M Bennett, S Siksek - Transactions of the American Mathematical Society, 2023 - ams.org
We develop a variety of new techniques to treat Diophantine equations of the shape $ x^ 2+
D= y^ n $, based upon bounds for linear forms in $ p $-adic and complex logarithms, the …
D= y^ n $, based upon bounds for linear forms in $ p $-adic and complex logarithms, the …
Some exponential Diophantine equations III: a new look at the generalized Lebesgue–Nagell equation
M Le, G Soydan - Boletín de la Sociedad Matemática Mexicana, 2024 - Springer
Let D be a fixed non-square integer, and let h (4 D) denote the class number of binary
quadratic primitive forms with discriminant 4 D. Let k be a fixed even integer with gcd (D, k) …
quadratic primitive forms with discriminant 4 D. Let k be a fixed even integer with gcd (D, k) …