Geodesic
On Equal Products of Consecutive Integers
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 255-259

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Using the theory of algebraic numbers, Mordell [1] has shown that the Diophantine equation 1 possesses only two solutions in positive integers; these are given by n = 2, m = 1, and n = 14, m = 5. We are interested in positive integer solutions to the generalized equation 2 and in this paper we prove for several choices of k and l that (2) has no solutions, in other cases the only solutions are given, and numerical evidence for all values of k and l for which max (k, l) ≤ 15 is also exhibited. 
Macleod, R. A.; Barrodale, I. On Equal Products of Consecutive Integers. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 255-259. doi: 10.4153/CMB-1970-052-8
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     title = {On {Equal} {Products} of {Consecutive} {Integers}},
     journal = {Canadian mathematical bulletin},
     pages = {255--259},
     year = {1970},
     volume = {13},
     number = {2},
     doi = {10.4153/CMB-1970-052-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-052-8/}
}
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