A necessary and sufficient condition is obtained for the uniform distribution modulo p of a sequence of integers satisfying a linear recurrence relation. Let A = la I' be an infinite sequence of integers. For integers n n =1 m > 2 and r, let A(N, r, m) denote the number of terms a such that n 2. Kuipers, Niederreiter, and Shiue [ 1], [ 21, ['41 have proved that the Fibonacci numbers are uniformly distributed modulo m only for m = 5k, and that the Lucas numbers are not uniformly distributed modulo m for any m > 2. Both the Lucas and Fibonacci numbers satisfy the linear recurrence xn+2 = xn+l + xn. In this note we consider the uniform distribution of an arbitrary linearly recurrent sequence of integers. Theorem 1. Let XI= IxnIn= be a sequence of integers satisfying the linear recurrence xn+2 = ax +1 + bx . Let p be an odd prime. Then the sequence X is uniformly distributed modulo p if and only if p l(a2 + 4b), p{a, and p{ (2x2 ax1). The sequence X is uniformly distributed modulo 2 if and only if 21a,2{b, and 2{(x2 -x1) Proof. The linearly recurrent sequence X is periodic modulo p. If the period of X is not divisible by p, then X is certainly not uniformly distributed modulo p. Zierler [51 showed that if p{ (a2 + 4b), then the period of X is relatively prime to p. If pI(a2 + 4b) and pla, then plb, and so xn 0 (mod p) for all n > 3. If pI(a2+ 4b) and p t a, then Presented to the Society, January 16, 1974 under the title Uniform distribution and linear recurrences; received by the editors February 4, 1974. AMS (MOS) subject classifications (1970). Primary 10A35, 10F99.