Question

Find all the integral solutions of the equation \(8y + 11x + 17 =xy\).

Answer 1

K, so what's y?

Answer 2

(11x + 17) / (x-8) = y , right?

Dunno if this is any good or not...

Answer 3

Need to break that up somehow....

Answer 4

11 + 105/(x-8)

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

It's x we want....

Answer 9

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?

Answer 10

Ther u go....

Answer 11

Then the y's

Answer 12

11 +

Answer 13

Thanks. :-)

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

Answer 14

In the actual question, that is.