41, k = 6. The question of the existence of intrinsic divisors when a and fi are real but not necessarily integers was studied some time ago in these Annals by R. D. Carmichael [3], and again quite recently by C. G. Lekkenkerker [6]. In this paper, I study the intrinsic divisors of D. H. Lehmer's generalization of the Lucas numbers [5] in which merely (a + p3)2 and afi are required to be integers, again under the assumption that a and fi are real. The method of attack goes back in principle to Sylvester [7], page 607, and is powerful enough to furnish a complete answer. Nothing appears to be known about the intrinsic divisors of Lucas or Lehmer numbers when a and d are complex. Let L and Ml be integers, with L and K = L - 4M positive and M 5 0. Then the roots a and ,3 of the polynomial