41. Yuri Matiyasevich utilized a method involving Fibonacci numbers, which computably enumerable set is Diophantine . 42. In the case of the linear diophantine equation 43. Generally, they are used in finding solutions of diophantine equations or to factor numbers. 44. His interests are in number theory, effective methods, Diophantine geometry and Diophantine analysis. 45. His interests are in number theory, effective methods, Diophantine geometry and Diophantine analysis. 46. Accordingly, the frequency resonance condition is equivalent to a Diophantine equation with many unknowns. 47. The field of Diophantine approximation deals with the cases of " Diophantine inequalities ". 48. The field of Diophantine approximation deals with the cases of " Diophantine inequalities ". 49. Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry ). 50. The Matiyasevich / MDRP theorem has shown that recursively enumerable sets are equivalent to Diophantine sets.