- #1

- 43

- 0

**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.