Ishaan94
Find all the integral solutions of the equation \(8y + 11x + 17 =xy\).



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estudier
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K, so what's y?

estudier
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(11x + 17) / (x8) = y , right?
Dunno if this is any good or not...

estudier
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Need to break that up somehow....

estudier
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11 + 105/(x8)

estudier
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So 105/(x8) must be integer......

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

Ishaan94
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105 = 5*7*3*1. So, 8 integral solutions? Am I doing it right?

estudier
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It's x we want....

Ishaan94
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5*7. 2 more.
5*3. 2 more.
7*3. 2 more.
and 105 itself. 2 more integral solutions.
I mean x8 could be \(\pm5,7,3,1,5*7,5*3,105,7*3\), Right?

estudier
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Ther u go....

estudier
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Then the y's

estudier
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11 +

Ishaan94
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Thanks. :)
Don't worry, I don't need the y's. I only need to show the total number of solutions are 16.

Ishaan94
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In the actual question, that is.