Bowman-Bradley type theorem for finite multiple zeta values

The multiple zeta values are multivariate generalizations of the values of the Riemann zeta function at positive integers. The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of twos between 3,1,...,3,1 add up to a rational multiple of a power of \pi. We show that an analogous theorem holds in a very strong sense for finite multiple zeta values, which have been investigated by Hoffman and Zhao among others and recently recast by Zagier.