## anonymous 3 years ago Find all the integral solutions of the equation $$8y + 11x + 17 =xy$$.

1. anonymous

K, so what's y?

2. anonymous

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

3. anonymous

Need to break that up somehow....

4. anonymous

11 + 105/(x-8)

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

It's x we want....

9. anonymous

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. anonymous

Ther u go....

11. anonymous

Then the y's

12. anonymous

11 +

13. anonymous

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

14. anonymous

In the actual question, that is.