A Multi-frey Approach to Some Multi-parameter Families of Diophantine Equations
نویسنده
چکیده
We solve several multi-parameter families of binomial Thue equations of arbitrary degree; for example, we solve the equation 5x − 23y = ±1, in non-zero integers x, y and positive integers u, r, s and n ≥ 3. Our approach uses several Frey curves simultaneously, Galois representations and level-lowering, new lower bounds for linear forms in 3 logarithms due to Mignotte and a famous theorem of Bennett on binomial Thue equations.
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