Rešite x^51+1=0

$${ x }^{ 51 } +1=0$$

Rešitev za x (complex solution)

$$x\in e^{\frac{3\pi i}{17}},e^{\frac{\pi i}{17}},e^{\frac{5\pi i}{17}},e^{\frac{7\pi i}{17}},e^{\frac{9\pi i}{17}},e^{\frac{11\pi i}{17}},e^{\frac{13\pi i}{17}},e^{\frac{15\pi i}{17}},-1,e^{\frac{19\pi i}{17}},e^{\frac{21\pi i}{17}},e^{\frac{23\pi i}{17}},e^{\frac{25\pi i}{17}},e^{\frac{27\pi i}{17}},e^{\frac{29\pi i}{17}},e^{\frac{31\pi i}{17}},e^{\frac{33\pi i}{17}},e^{\frac{5\pi i}{51}},e^{\frac{11\pi i}{51}},e^{\frac{\pi i}{3}},e^{\frac{23\pi i}{51}},e^{\frac{29\pi i}{51}},e^{\frac{35\pi i}{51}},e^{\frac{41\pi i}{51}},e^{\frac{47\pi i}{51}},e^{\frac{53\pi i}{51}},e^{\frac{59\pi i}{51}},e^{\frac{65\pi i}{51}},e^{\frac{71\pi i}{51}},e^{\frac{77\pi i}{51}},e^{\frac{83\pi i}{51}},e^{\frac{89\pi i}{51}},e^{\frac{95\pi i}{51}},e^{\frac{101\pi i}{51}},e^{\frac{\pi i}{51}},e^{\frac{7\pi i}{51}},e^{\frac{13\pi i}{51}},e^{\frac{19\pi i}{51}},e^{\frac{25\pi i}{51}},e^{\frac{31\pi i}{51}},e^{\frac{37\pi i}{51}},e^{\frac{43\pi i}{51}},e^{\frac{49\pi i}{51}},e^{\frac{55\pi i}{51}},e^{\frac{61\pi i}{51}},e^{\frac{67\pi i}{51}},e^{\frac{73\pi i}{51}},e^{\frac{79\pi i}{51}},e^{\frac{5\pi i}{3}},e^{\frac{91\pi i}{51}},e^{\frac{97\pi i}{51}}$$

Rešitev za x

$$x=-1$$