Who knows algorithms well?

Question

Mathematics

There is this expression:

a + b = a * b

What are the values ​​of a and b?
The answer can be seen immediately - it's two and two. Since a and b are integers, and if we take just a search, then the only value is 2.

2 + 2 = 2 * 2

It doesn’t even take 10 seconds to answer.
But how to write it mathematically? And how to write a iteration cycle programmatically?

Answer 1

This is solved analytically.
a + b = a b
a + b - a b = 0
a (1 - b) + b = 0
a = b / (b - 1)
Obviously, this fraction will be an integer only in two cases,
b - 1 = -1, b = 0, a = 0
b - 1 = 1, b = 2, a = 2

Answer 2

The graphical calculator suggests that there are infinitely many solutions, and they lie on two parabolas.
The inclined plane is the sum, the "saddle" is the product. Their intersection is where they are equal.

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