a^n + b^n = c^2

Let n be a natural number such that the equation

a^n + b^n = c^2

where a, b and c are prime numbers has at least one solution.

Find the maximal possible value of n

Hint: if n = 1 => there is a solution a = 7, b = 2, c = 3.

Now, if n > 1, then what?