Claude Gaspar Bachet de Méziriac

Claude Gaspar Bachet Sieur de Méziriac (9 October 1581 – 26 February 1638) was a French mathematician and poet born in Bourg-en-Bresse, at that time belonging to Duchy of Savoy. He wrote Problèmes plaisans et délectables qui se font par les nombres, Les éléments arithmétiques, and a Latin translation of the Arithmetica of Diophantus (the very translation where Fermat wrote a margin note about Fermat's Last Theorem). He also discovered means of solving indeterminate equations using continued fractions, a method of constructing magic squares, and a proof of Bézout's identity. Claude Gaspar Bachet de Méziriac was born in Bourg-en-Bresse. By the time he reached the age of six, both his mother (Marie de Chavanes) and his father (Jean Bachet) had died. He was then looked after by the Jesuit Order. For a year in 1601, Bachet was a member of the Jesuit Order (he left due to an illness). Bachet lived a comfortable life in Bourg-en-Bresse. He married Philiberte de Chabeu in 1620 and had seven children. Bachet was a pupil of the Jesuit mathematician Jacques de Billy at the Jesuit College in Rheims. They became close friends. Bachet wrote the Problèmes plaisans et délectables qui se font par les nombres of which the first edition was issued in 1612, a second and enlarged edition was brought out in 1624; this contains an interesting collection of arithmetical tricks and questions, many of which are quoted in W. W. Rouse Ball's Mathematical Recreations and Essays. He also wrote Les éléments arithmétiques, which exists in manuscript; and a translation, from Greek to Latin, of the Arithmetica of Diophantus (1621). It was this very translation in which Fermat wrote his famous margin note claiming that he had a proof of Fermat's Last Theorem. The same text renders Diophantus' term παρισὀτης as adaequalitat, which became Fermat's technique of adequality, a pioneering method of infinitesimal calculus. Bachet was the earliest writer who discussed the solution of indeterminate equations by means of continued fractions.

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Claude Gaspar Bachet de Méziriac

Pierre de Fermat

Pierre de Fermat (pjɛʁ də fɛʁma; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory.

Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of Arithmetica. Fermat added that he had a proof that was too large to fit in the margin.

Polynomial Methods: GCD Calculation Summary

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.