Joe Root his first golden duck in his ODI career. The 5th ODI was better for Root as he scored a quick 21 before being bowled and also took the wicket of George Bailey. England lost the series 2–1 and Root finished the series with 36 runs and 1 wicket. Root was selected for the 2013-14 Ashes series. He was selected at number 6 for the first Test as Michael Carberry was given the opening batsman role alongside Alastair Cook. Root only managed 2 runs from 7 balls in the first innings before being caught off a Mitchell Johnson delivery. In the
Root of unity modulo n a primitive formula_25-th root of unity because there is the smaller exponent formula_72. That is, by exponentiating "x" one can obtain formula_84 different primitive "k"-th roots of unity, but these may not be all such roots. However, finding all of them is not so easy. You may want to know, in what integer residue class rings you have a primitive "k"-th root of unity. You need it for instance if you want to compute a Discrete Fourier Transform (more precisely a Number theoretic transform) of a formula_25-dimensional integer vector. In order to perform the inverse transform, you also need to