Abstract
AbstractWe solve several multi-parameter families of binomial Thue equations of arbitrary degree; for example, we solve the equation5uxn − 2r3s yn = ±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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