@article{Dong2023, 
author = {Ziyu Dong and Zhengjun Zhao},
title = {An application of    p-adic Baker method to a special case of Jeśmanowicz' conjecture},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {5},
pages = {11617-11628},
keywords = {exponential Diophantine equation, Pythagorean triple, Jeśmanowicz' conjecture},
url = {https://www.sciopen.com/article/10.3934/math.2023588},
doi = {10.3934/math.2023588},
abstract = {In 1956, Jeśmanowicz conjectured that, for any positive integer    n, the Diophantine equation              (              (                  f                      2                          −                  g                      2                          )        n            )              x        +            (              (        2        f        g        )        n            )              y        =            (              (                  f                      2                          +                  g                      2                          )        n            )        z   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  =  6  k  +  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.}
}