Geodesic
A lower bound on the time complexity of an integer problem on the uniqueness of elements
Diskretnaya Matematika, Tome 3 (1991) no. 3, pp. 31-34 
L. V. Nosov. A lower bound on the time complexity of an integer problem on the uniqueness of elements. Diskretnaya Matematika, Tome 3 (1991) no. 3, pp. 31-34. http://geodesic.mathdoc.fr/item/DM_1991_3_3_a2/
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     author = {L. V. Nosov},
     title = {A~lower bound on the time complexity of an integer problem on the uniqueness of elements},
     journal = {Diskretnaya Matematika},
     pages = {31--34},
     year = {1991},
     volume = {3},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1991_3_3_a2/}
}
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We consider an integer problem on the uniqueness of elements which we formulate as follows: Check whether there exists among $n$ given integers at least one pair equal to each other. We prove that $\Omega (n\log n)$ is the lower bound on the time complexity of this problem in a model of a linear solution tree. We obtain lower bounds on the time complexity of several geometric problems to which it reduces.