  This paper considers the problem of the valuation for integer numbers of the
zeta function and of five other functions which are naturally associated to it.
A relatively elementary approach is exposed, which closely connects this still
partially open problem to five themes of parity: the notions of parity of a
function and of parity of the degree of a polynomial are here related to the
distinctions of parity concerning the natural argument of the six considered
functions as well as the integer numbers of which some inverse powers are
summed. The adopted method essentially aims at enabling the students in
mathematics to have an entry into this problem.
