13th root 13th root of a 100-digit number. All world records for mentally extracting a 13th root have been for numbers with an integer root. 13th root Extracting the 13th root of a number is a famous category for the mental calculation world records. The challenge consists of being given a large number (possibly over 100 digits) and asked to return the number that, when taken to the 13th power, equals the given number. For example, the 13th root of 8,192 is 2 and the 13th root of 96,889,010,407 is 7. Extracting the 13th root has certain properties. One is that 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