Geodesic
Remarks on a Problem of Obreanu
Canadian mathematical bulletin, Tome 6 (1963) no. 2, pp. 267-273

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Let a1 < a2 < ... be any sequence of integers. Assume that the infinite sequence of numbers un satisfies the following condition: To every ɛ > 0 there is an no = no (ɛ) such that for all n > no and all k 1 Obreanu asked (Problem P. 35 Can. Math. Bull.) under what conditions on the sequence a1 < a2 < ... does (1) imply that the sequence u is convergent. N. G. de Bruijn and P. Erdos proved that a necessary and sufficient condition for (1) to imply the convergence of un is that the sequence {an} be infinite and that the greatest common divisor of the a1 should be 1. 
Erdös, P.; Rényi, A. Remarks on a Problem of Obreanu. Canadian mathematical bulletin, Tome 6 (1963) no. 2, pp. 267-273. doi: 10.4153/CMB-1963-024-5
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     title = {Remarks on a {Problem} of {Obreanu}},
     journal = {Canadian mathematical bulletin},
     pages = {267--273},
     year = {1963},
     volume = {6},
     number = {2},
     doi = {10.4153/CMB-1963-024-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-024-5/}
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