# An algebra problem by Shriram Lokhande

**Algebra**Level 3

Define \(\varrho(n)\) be a function which gives product of roots of the equation \[\sqrt{n}^x+\frac{1}{\sqrt{n}^x}=2\] where \(n\) is a gaussian integer .

Find \[\prod_{gaussian integers}{\varrho(n)}\]

**Details**

gaussian integer is an complex number \(a+bi\) where a and b as integers