- #1
MSG100
- 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 a lot 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.
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 a lot 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.