**Explanation:**

Let Q = n (n + 1). It is convenient to choose n = m^{2}, for then Q is already a sum of two squares: Q = m^{2}(m^{2} + 1) = (m^{2})^{2} + m^{2}. If further m^{2} itself is a sum of two square, say m^{2} = p^{2} + q^{2}, then

Q = (p^{2} + q^{2})(m^{2} + 1) = (pm + p)^{2} + (p - qm)^{2}.

That the two representation or Q are distinct. Thus for example, we may take m = 5k, p = 3k, q = 4k, where k varies over natural numbers. In this case n = m^{2} = 25k^{2},

Q = (25k^{2})^{2} + (5K^{2})^{2} = (15k^{2} + 4k)^{2} + (20k^{2} - 3k)^{2}.

Every k over natural number, we get infinitely many numbers the form n(n + 1) which can be expressed as a sum two squares in two distinct ways.