RECIPES FOR TERNARY DIOPHANTINE EQUATIONS OF SIGNATURE (p, p, k)
نویسنده
چکیده
In this paper, we survey recent work on ternary Diophantine equations of the shape Axn + Byn = Czm for m ∈ {2, 3, n} where n ≥ 5 is prime. Our goal is to provide a simple procedure which, given A, B, C and m, enables us to decide whether techniques based on the theory of Galois representations and modular forms suffice to ensure that corresponding ternary equations lack nontrivial solutions in integers x, y, z and prime n ≥ 5.
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