13th 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 13th root of a number is much smaller: a 13th root will have approximately 1/13th the number of digits. Thus, the 13th root
Primitive root modulo n adding up elements of this multiplicative group? As it happens, sums (or differences) of two primitive roots add up to all elements of the index 2 subgroup of Z/"n" Z for even "n", and to the whole group Z/"n" Z when "n" is odd: No simple general formula to compute primitive roots modulo "n" is known. There are however methods to locate a primitive root that are faster than simply trying out all candidates. If the multiplicative order of a number "m" modulo "n" is equal to formula_2 (the order of Z), then it is a primitive root. In fact