Algebra Explained

What is a diophantine equation?

The first mention of diophantine equations was by Greek (Hellenic) mathematician Diophantus (c. 210-c. 290 C.E.). In his treatise Arithmetica, he solved equations with several variables for integral solutions—or what we call diophantine equations today. (For more about Dio-phantus in history, see “History of Mathematics.”) These are represented by one equation with at least two variables, such as x and y, and whose solutions have to be whole numbers (or integers). These equations either have no solutions, or an infinite or finite number of solutions. Diophantine analysis is the mathematical term for how to determine integer solutions for such algebraic equations.


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