E-resources
Peer reviewed
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Yang, Hai; Fu, Ruiqin
Periodica mathematica Hungarica, 09/2019, Volume: 79, Issue: 1Journal Article
Let p be an odd prime. By using a lower bound for linear forms in logarithms of two algebraic numbers, we prove that if p > 10 24 , 2 is a primitive root module p and the least solution ( u 1 , v 1 ) of Pell’s equation u 2 - 2 ( p - 1 ) ( p - 2 ) v 2 = 1 satisfies log u 1 + v 1 2 ( p - 1 ) ( p - 2 ) < p 2 3 , then the equation x m - 1 x - 1 = y n - 1 y - 1 has no positive integer solutions ( x , y , m , n ) with x = 2 , y = p and m > n > 2 .
