ProjectEuler 479 Roots on the Rise - 拼圖

479. Roots on the Rise

https://projecteuler.net/problem=479

令 a_k, b_k, c_k 為方程式 1/x = (k/x)^2 (k+x^2) - kx 的三個解 (含實數及複數)。

例如當 k = 5 時，{a_k, b_k, c_k} 的近似值為 {5.727244, -0.363622+2.057397i,
-0.363622-2.057397i}。

令 S(n) = Σ(a_k+b_k)^p (b_k+c_k)^p (c_k+a_k)^p,

其中 p, k 為整數, 滿足 1≦p,k≦n。

有趣的是，S(n) 永遠是整數，如 S(4) = 51160。

求 S(10^6) mod 1 000 000 007。

--
'Oh, Harry, don't you see?' Hermione breathed. 'If she could have done
one thing to make absolutely sure that every single person in this school
will read your interview, it was banning it!'
---'Harry Potter and the order of the phoenix', P513

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