Cyclotomic fields like the Eisenstein integers are constructed by adjoining one of these values to the rational numbers. The discrete logarithm exists for all integers modulo n if and only if the base of the logarithm is one of these values, since those examples of these values generate the multiplicative groups of integers modulo n. A common divisibility test for (*) nine involves calculating one of these values by summing the digits of an integer. According to the Abel-Ruffini theorem, for polynomials of degree higher than five, these values cannot be expressed solely in terms of radicals. For 10 points, “primitive” and “digital” describe what kinds of values in mathematics, also exemplified by i, a “square” one of these values for negative one. ■END■
ANSWER: roots [accept primitive roots modulo ns; accept digital roots; accept roots of a polynomial; accept square roots; prompt on zeroes or solutions of a polynomial after “Abel-Ruffini”]
<IC, Mathematics>
= Average correct buzz position