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International audienceIn this paper, we give a new Salem number with degree 34 and trace −3, whereas the Salem number of lower degree known up to now, with trace −3 , was of degree 54. The method used to find this Salem number also provides a list of 41 monic integer polynomials of smallest possible trace, irreducible, with degree 17, and having all roots real and positive. Moreover, we think that this list may be complete

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