Determine the remainder when x1000x^{1000}x1000 is divided by x2−3x+2x^2 - 3x + 2x2−3x+2.
(21000−1)x−(21000−2)(2^{1000}-1)x - (2^{1000}-2)(21000−1)x−(21000−2)
(21000−1)x+21000(2^{1000}-1)x + 2^{1000}(21000−1)x+21000
(21000−1)x+1(2^{1000}-1)x + 1(21000−1)x+1
2^{1000}x - 1