## Ishaan94 Group Title Find all the integral solutions of the equation $$8y + 11x + 17 =xy$$. 2 years ago 2 years ago

1. estudier

K, so what's y?

2. estudier

(11x + 17) / (x-8) = y , right? Dunno if this is any good or not...

3. estudier

Need to break that up somehow....

4. estudier

11 + 105/(x-8)

5. estudier

So 105/(x-8) must be integer......

6. estudier

Exhaustion/look for a pattern takes care of that, I think...

7. Ishaan94

105 = 5*7*3*1. So, 8 integral solutions? Am I doing it right?

8. estudier

It's x we want....

9. Ishaan94

5*7. 2 more. 5*3. 2 more. 7*3. 2 more. and 105 itself. 2 more integral solutions. I mean x-8 could be $$\pm5,7,3,1,5*7,5*3,105,7*3$$, Right?

10. estudier

Ther u go....

11. estudier

Then the y's

12. estudier

11 +

13. Ishaan94

Thanks. :-) Don't worry, I don't need the y's. I only need to show the total number of solutions are 16.

14. Ishaan94

In the actual question, that is.