An application of p-adic Baker method to a special case of Jes´manowicz’ conjecture
An application of p-adic Baker method to a special case of Jes´manowicz’ conjecture
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DOI：
10.3934/math.2023588
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发表时间：
2023
期刊：
影响因子：
2.2
通讯作者：
赵正俊
中科院分区：
文献类型：
--
作者：
Ziyu Dong;赵正俊
In 1956, Jesmanowicz conjectured that, for any positive integer ´ n, the Diophantine equation.has only the positive integral solution (x, y,z) = (2, 2, 2), where.f and g are positive integers with f > g, gcd(f, g) = 1, and f . g (mod 2). Let r = 6k + 2, k ∈ N,.k ≥ 25. In this paper, combining p-adic form of Baker method with some detailed computation, we.prove that if n satisfies n ≡ 0, 6, 9 (mod 12), f = g + 1 and g = 2.r − 1, then the conjecture is true..
