Résumé: It is proved that the system of word equations x(1)(i) = y(1)(i)y(2)(i)y(n)(i), i = 1, 2, ..., [n/2+1, has only cyclic solutions. Some sharpenings concerning the cases n = 5, 7 and n⩾9 are derived as well as results concerning the general system of equations x(1)(i)x(2)(i)x(m)(i) = y(1)(i)y(2)(i)y(n)(i), i = 1, 2, ... . Applications to test sets of certain bounded languages are considered.

Langue: Anglais