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Diophantus ofAlexandria (~200 -- ~284) is known for Arithmetica, a work with 13 books and 189 problems on the solution of algebraic equations and on the theory of numbers. He studied determinate equations (unique solution) and indeterminate equations (set of solutions). A Diophantine equation is a polynomial equation with integral coefficients to which only integral solutions are considered. Diophantus looked at three types of quadratic equations: ax2 + bx = c, ax2 = bx + c and ax2 + c = bx. Diophantus considered these three cases (today we consider them the same case) because he did not have a notation for zero and he avoided negative coefficients. He considered negative or irrational square root solutions useless, meaningless,or absurd. The simplest Diophantine equation is the linear equation ax + by = c. Diophantus was famous for a riddle about his life, supposedly carved on his tombstone. In 1637, while reviewing his translated copy of Diophantus' Arithmetica, Pierre de Fermat wrote his famous "Last Theorem" in the page's margins. His copy with his margin-notes survives to this day. |