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MODULO ONE UNIFORM DISTRIBUTION 294 OF CERTAIN FIBONACCI-RELATED SEQUENCES Apr. 1972 [Continued from page 280. ] is also uniformly distributed mod 1 and the mod 1 uniform distribution of In V then follows from (2) in conjunction with Lemma 1. q. e, d„ In F ) and (In L j are uniformly d i s - tributed mod 1. Here { F J = {l, 1, 2, 3, ...} and ( L J = (2, 1, 3, 4, • • •} are the Fibonacci and Lucas sequences, respectively,, Proof, n ^ 1 with Both sequences satisfy the r e c u r s i o n V 2 =V - +V for (Ki9 K 2 ) = (1,1) for the Fibonacci sequence and (Kl9 K 2 ) = (2,1) for the Lucas sequence, so that the result follows directly from the theorem. REFERENCES 1. I. Niven, "Irrational Numbers," Carus Mathematical Monograph Number 11, The Math. Assn. of America, John Wiley and Sons, Inc. , New York, 2. P. R. Halmos, Measure Theory, D. Van Nostrand Co* , Inc., New York, New York, 1950, Renewal notices, normally sent -out to subscribers in November or December, are now sent . by bulk mail. This means that If your address has changed the notice will not be forwarded to you. If you have a change of address, please notify: Brother Alfred Brousseau St. Mary f s College St. Mary s s College, Calif.