Solving the system of n symmetric equations

I want to solve the following n symmetric equations. I am attaching the screenshot below. I want to solve the equation number 29 in an article. If you cannot see the screenshot, I am providing the link to the article below. Equation 29 in the article. How can I solve such an equation system in Mathematica?

As written it doesn’t make sense. The ‘j’ cannot be both an index and a dummy variable. Possibly this is only an error in exposition though.