Diophantus of Alexandria (dates unknown, lived and died between 200AD and 300AD) was an Alexandrian

mathematician.
He wrote a

series of books (many now lost) called

Arithmetica that deal with solving

algebraic equations.

Pierre de Fermat studied

Arithmetica and it was in the margin in his copy that he made the fateful
note in 1637 that a certain

equation similar to the Pythagorean

equation considered by Diophantus has no solutions,
and he found "a truly marvelous

proof of this proposition", the celebrated

Fermat's Last Theorem. This led to
tremendous advances in

number theory, and the study of

diophantine equations ("diophantine

geometry") and of
diophantine approximations remain important areas of mathematical research. Diophantus was the first Greek

mathematician
who recognized fractions as

numbers; thus he allowed positive

rational numbers for the coefficients and solutions.

In modern use, diophantine equations are usually algebraic equations with integer coefficients, for which integer
solutions are sought.

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