| 41. | In 2012 he was awarded the Lester Randolph Ford Award jointly with Thomas Ward for their work in diophantine equations.
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| 42. | A polynomial equation for which one is interested only in the solutions which are integers is called a Diophantine equation.
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| 43. | For a version of the linear diophantine equation with solutions in natural numbers, this gives the following system of equations.
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| 44. | An integer constraint leads to integer programming and Diophantine equations problems, which may have only a finite number of solutions.
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| 45. | He created a new algebraic notation system and, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations.
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| 46. | Already in the 1920s Thoralf Skolem showed that any Diophantine equation is equivalent to one of degree 4 or less.
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| 47. | They also include famous cases like the Fermat curves, and other examples well known in the theory of Diophantine equations.
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| 48. | While the algorithm for solving a Diophantine equation you describe exists, it lacks ( in general ) a correctness proof.
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| 49. | Continued fractions can also be applied to problems in number theory, and are especially useful in the study of Diophantine equations.
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| 50. | The equation was eventually solved by Euler in the early 18th century, who also solved a number of other Diophantine equations.
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