A metal pipe designed to be placed within a well for producing a fluid of interest, on the outer face of which is crimped a tubular metal element, in which: - the inner face of said tubular element exhibits an annular groove wherein is engaged a metal anchoring ring or a pair of anchoring rings set back-to-back; - each anchoring ring (8, 8') consists of a ring at least partially slit transversely, is provided on its inner face (81, 81') with projecting anchoring members (810, 810'), and exhibits, in cross-section, a base (81, 81') provided with said projecting members (810, 810') and at least one flank (82, 82') forming an acute angle (α) with said base (81, 81'); - the annular groove exhibits a profile that is substantially complementary to that of the ring or of the pair of rings; - the depth (a) of the groove being less than the thickness (b) of the ring or of the rings; such that said projecting members (810, 810') are at least partially engaged in said pipe after crimping of the metal element onto the pipe, characterized in that: - when a single ring is engaged in said groove, said ring includes a transverse slit constituting an interruption in the material and in that said ring has a second flank, these two flanks being separated from one another by a face that is substantially parallel to said base such that the ring assumes, in cross-section, the general shape of a trapezoid, said acute angles (α) being equal, such that said ring assumes, in section, a symmetrical shape, or - when a pair of identical anchoring rings is engaged in said groove, each ring includes a series of partial transverse slit, the second ring of the pair having a second flank, so that the two flanks (82, 82') of the pairs are separated from one another by a face that is substantially parallel to said base such that the pair of rings assumes, in cross-section, the general shape of a trapezoid, said acute angles (α) being equal, such that said pair of rings assumes, in section, a symmetrical shape. - the inner face of said tubular element exhibits an annular groove wherein is engaged a metal anchoring ring or a pair of anchoring rings set back-to-back; - each anchoring ring (8, 8') consists of a ring at least partially slit transversely, is provided on its inner face (81, 81') with projecting anchoring members (810, 810'), and exhibits, in cross-section, a base (81, 81') provided with said projecting members (810, 810') and at least one flank (82, 82') forming an acute angle (α) with said base (81, 81'); - the annular groove exhibits a profile that is substantially complementary to that of the ring or of the pair of rings; - the depth (a) of the groove being less than the thickness (b) of the ring or of the rings; - when a single ring is engaged in said groove, said ring includes a transverse slit constituting an interruption in the material and in that said ring has a second flank, these two flanks being separated from one another by a face that is substantially parallel to said base such that the ring assumes, in cross-section, the general shape of a trapezoid, said acute angles (α) being equal, such that said ring assumes, in section, a symmetrical shape, or - when a pair of identical anchoring rings is engaged in said groove, each ring includes a series of partial transverse slit, the second ring of the pair having a second flank, so that the two flanks (82, 82') of the pairs are separated from one another by a face that is substantially parallel to said base such that the pair of rings assumes, in cross-section, the general shape of a trapezoid, said acute angles (α) being equal, such that said pair of rings assumes, in section, a symmetrical shape.