Sum = Product = Quotient

'Sum = Product = Quotient' printed from https://nrich.maths.org/

How many pairs of numbers $(a,b)$ exist such that the sum $a+b$, the product $ab$, and the quotient $\frac{a}{b}$ are all equal?

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.