Analytical Solution of Some Higher Degree Equation Via Radicals

Since the advent of diophantine equations, many dierent analytic solutions have been formulated for equations with degree n
4. However, little has been documented on solvability of equation of degree n
5 via the radicals. The majority of recent research seem to have put more focus towards numerical solutions, possibly due to the fact that quintic equations have been proved to be insoluble via the radicals. Let u and v be any non negative integers. This study delves into realm of analytical solutions of some higher degree equation of the form + = uv where u and v are relatively prime.The method of the study involves use of radical solution using case to case basis. In particular,the solution of the equation
+ = uv for n = 1 and n = 2 where u and v are relatively prime is completely determined.