  Let K/Q be a cyclic extension. In this paper, we give several congruences
connecting the prime divisors of the degree g= [K:Q] with the prime divisors of
the class number h of K/Q. As an exemple, the theorem:
  Let K/Q be a cyclic extension with [K:Q]=g. Suppose that g is not divisible
by 2 .
  Let g_j, j=1,...m, be the prime divisors of g.
  Let h_i, i=1,...r, be the prime divisors of the class number h of K/Q.
  If for one prime factor h_i of h, the h_i-component G(h_i) of the class group
G of K/Q is cyclic then: else h_i divides g, else h_i = 1 (mod g_j) for at
least one prime divisor g_j of g. The results obtained are all in accordance
with class number tables of Washington, Masley, Girtsmair, Schoof, Jeannin and
number fields server megrez.math.u-bordeaux.fr The proofs are strictly
elementary.
