# 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

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