How does a universal Turing machine function? Explain with an example. Design an algorithm for finding integer solutions for equations of the form x^2 + y^2 = n, where n is some given positive...

How does a universal Turing machine function? Explain with an example. Design an algorithm for finding integer solutions for equations of the form x^2 + y^2 = n, where n is some given positive integer. Determine the time complexity of your algorithm.