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