Can You Solve This Soviet Math Equation?

This was sent to me by a friend from Russia

The problem we are looking at today is from an old Soviet math textbook, specifically we are looking at question 46 which involves a nested expression with 1964 radicals.

Решите в целых числах уравнение

Translate into English, that is

Solve the equation in integers

Here’s a clearer look of the problem. Now grab your pen and paper to give this a go, when you are ready, scroll down for the solution!