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Publication
of Emmanuel Peyre

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[1] Des Nombres... au hasard, Séminaire du magistère, Institut Fourier, Grenoble (5th Novembre 2016)

Integral solutions of polynomial equations in several variables are considered since the beginning of mathematics, as shown by babylonian tablets with lists of pythagorean triples. A more recent approach aims to study the set of solutions, when it is infinite, from the point of view of the theory of probability. But the study of many examples shows that these solution do not behave as randomly as one may expect.