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I need help with this question:

Determine the number of distinct pairs $(a,b) \in \mathbb{Z}_{>0}\times\mathbb{Z}_{>0}$ of positive integers satisfying the equation:

$360(a+b)=ab$

For a start, I do observe that ab must be a multiple of 360. But how do I proceed from here? Any advice would be greatly appreciated.

Soby
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1 Answers1

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Here's one approach to the problem.

Rewrite: $ab-360a-360b=0$.

Add something so that the left side can be factored: $ab-360a-360b+360^2=360^2$

Then $(a-360)(b-360)=360^2$.

Go on from there.

paw88789
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