Problem: Find all the positive integer solutions where x and y are odd numbers, to the equation: 17x+11y=1000 Attempt of solution: First attempt: With Diophantine equation have gotten the answers: x=2000 y=-3000 and the general solutions will be: x=2000-11k y=-3000+17k Now I don't know what to do. Second attempt: If I skip the Diophantine solution and do it like this: y=(1000-11x)/17 Now I see that x has to be in the interval 0≤x≤58 if y should be positive. If I test all the odd numbers in the interval I'll get 3 solutions when both x and y are positive and odd numbers. The solutions are: (x, y) = (9, 77), (31, 43) and (53, 9) This solutions (which should be the right answer) takes alot of time because you have to test all odd numbers between 0 to 58 (29 different numbers). I need help to find an easier solution.