科研之友
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摘要
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 > 1024, 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) root 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.
