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He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events.
As noted before, his first attempt was refused by Cauchy, but in February 1830 following Cauchy's suggestion he submitted it to the Academy's secretary Fourier, to be considered for the Grand Prix of the Academy.
Unfortunately, Fourier died soon after, and the memoir was lost.
The prize would be awarded that year to Abel posthumously and also to Jacobi.
Despite the lost memoir, Galois published three papers that year, one of which laid the foundations for Galois theory.
The second one was about the numerical resolution of equations ( root finding in modern terminology ).
The third was an important one in number theory, in which the concept of a finite field was first articulated.

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