[math-fun] Sum of squares formula

For integer n >= 0, we know F(n) := Sum_{1 <= k <= n} k^2 = n(n+1)(2n+1)/6 (= n^3/3 + n^2/2 + n/6) . It's also well known that if F(n) is an integer square, the only integer solutions are (n, F(n)) in {(0, 0), (1, 1), (24, 70^2)}. QUESTION: --------- What are the rational solutions p/q, s/t to the equation F(p/q) = (s/t)^2 ??? Or in other words, solutions p, q, s, t to the Diophantine equation (2p^3 + 3p^2 q + p q^2) t^2 = 6q^3 s^2 --Dan