Étienne Bézout (31 March 1730 to 27 September 1783) was a French mathematician, born in Nemours, Seine-et-Marne, who died in Avon near Fontainebleau. He was the second son of Pierre Bézout and Jeanne-Hélène Filz, from a family whose men had served as district magistrates, and he was deeply influenced by Leonhard Euler at an early age. In 1758, at the age of 19, he was elected an adjoint in mechanics of the French Academy of Sciences. In 1763 he accepted the post of mathematics teacher and examiner of the Gardes de la Marine, for which he composed a textbook to teach mathematics to naval cadets. He is also acknowledged for his work on algebra, publishing papers on algebraic equations, the theory of equations and elimination theory.
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His family was well-connected politically, and both his father and grandfather had served as district magistrates.
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In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout who proved it for polynomials, is a theorem which relates two arbitrary integers with their greatest common divisor.
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It is named after Étienne Bézout.
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