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very useful problem
By karimok, history, 9 years ago, translation, In English

Hello everybody)

help me with problem

we looking for quantity of integer solutions (x,y) equation ; |a|,|b| <=

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9 years ago, # |
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I found this:

a.y + b.x = x.y

b.x = y.(x-a)

y=(b.x) / (x-a);

x,y are integers so (a|b means b%a=0)

x-a| b.x

x-a| b.x — b.(x-a)

x-a| b.x — b.x + a.b

x-a| a.b

for every z (z|a.b) there is an integer pair (x,y) suitable to all conditions. So the answer is same with quantity of divisors of a.b

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