困難對數函數問題 http://i707.photobucket.com/albums/ww74/stevieg90/IMG_6180_zpsqcv9l5ox.jpg?

　　　　　　　　　　　 2014

x = ────────────────────────────────

　　(√2015 + 1)(∜2015 + 1)(⁸√2015 + 1)(¹⁶√2015 + 1)

Let ¹⁶√2015 = k , then

x = (k¹⁶ - 1) / [(k⁸ + 1)(k⁴+ 1)(k² + 1)(k + 1)]

x = (k⁸ - 1)(k⁸ + 1) / [(k⁸ + 1)(k⁴+ 1)(k² + 1)(k + 1)]

x = (k⁴- 1)(k⁴+ 1)(k⁸ + 1) / [(k⁸ + 1)(k⁴+ 1)(k² + 1)(k + 1)]

x = (k² - 1)(k² + 1)(k⁴+ 1)(k⁸ + 1) / [(k⁸ + 1)(k⁴+ 1)(k² + 1)(k + 1)]

x = (k - 1)(k + 1)(k² + 1)(k⁴+ 1)(k⁸ + 1) / [(k⁸ + 1)(k⁴+ 1)(k² + 1)(k + 1)]

x = k - 1

x + 1 = k

(x + 1)²º¹⁶ = k²º¹⁶

(x + 1)²º¹⁶ = ¹⁶√2015 ²º¹⁶

(x + 1)²º¹⁶ = 2015¹²⁶

2015ⁿ = 2015¹²⁶

n = 126