A Diophantine Equation

x² + y² - k*x*y = 1 (1) where k is an integer > 1 and 0 < x < y Let pol(n) be a monic polynomial of degree n: kⁿ + a_n-1*k^n-1 + ... + a₁*k + a₀ If the first solution to the above equation (1) is (1,k) pair then the solution to n_th would be (pol(n-1),pol(n)). What is the 100_th solution? Answer format: sum₁+sum₂ where sum₁=∑a_i³ for pol(99) and sum₂=∑a_i³ for pol(100) Example: -17402 (875-18277) for 10_th solution [My timing: < 1s] See also: Monic polynomial - Wikipedia, the free encyclopedia Diophantine equation - Wikipedia, the free encyclopedia