Explicit Methods for Solving Diophantine Equations

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Almost as many methods to solve Diophantine equations as equations. Attempt at classification: • Local methods: the use of p-adic fields, in an elementary way (congruences modulo powers of p), or less elementary (Strassmann’s or Weierstrass’s theorem, p-adic power series,Herbrand’s and Skolem’s method). • Factorization over Z.

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