  For each positive integer n, we determine the set of symmetric functions f
for which the congruence f(p/1,p/2,...,p/(p-1)) \equiv 0 mod p^n holds for all
sufficiently large primes p. Our determination is conditional on a conjecture
regarding the modulo p independence of Bernoulli numbers. In a recent work the
author introduced a new truncated analogue of the multiple zeta function and
investigated a class of relations among values of this function at positive
integers. The question answered in the present work is equivalent to the
determination of the relations satisfied by values of the corresponding
analogue of the ordinary Riemann zeta function.
