a^2 + ab + b^2 = n^2

(a+b)^2 = n^2 + ab

(a+b+n)(a+b-n) = ab

as 'a' and 'b' are prime numbers

ab has 4 factors: 1, a, b, ab

obviously, a + b + n > a + b - n

Case 1:

a + b + n = ab

a + b - n = 1

Case 2:

a + b + n = a

a + b - n = b ... considering a>b

But, case 2 is not possible.

b = -n

a = n,

a = -b ... which is impossible

Case 1:

adding the two equations

2a + 2b = ab + 1

2a - ab + 2b = 1

a(2-b) - 2(2-b) = -3

(a-2)(b-2) = 3

only possibility for 'a' and 'b' being prime and satisfying the above condition is: 5 and 3

giving us he only possibility 49