On a Problem of Brocard |
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| Authors: | Gica Alexandru; Panaitopol Laurentiu |
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| Institution: | University of Bucharest 14 Academiei St., RO-010014 Bucharest, Romania alex{at}al.math.unibuc.ro, pan{at}al.math.unibuc.ro |
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| Abstract: | It is proved that, if P is a polynomial with integer coefficients,having degree 2, and 1 >  > 0, then n(n – 1) ...(n – k + 1) = P(m) has only finitely many natural solutions(m,n,k), n  k > n, provided that the abc conjecture is assumedto hold under Szpiro's formulation. 2000 Mathematics SubjectClassification 11D75, 11J25, 11N13. |
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