On the diophantine equation x(x + 1)(x + 2)…(x + (m − 1)) =g(y) |
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| Authors: | Manisha Kulkarni |
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| Affiliation: | a Institut de Mathematiques de Bordeaux, Université Bordeaux I, 351, Cours de la Liberation, F-33405, Talence Cedex, France
b Stat-Math Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore - 560 059, India |
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| Abstract: | Let g(y) ? Q[Y] be an irreducible polynomial of degree n ≥ 3. We prove that there are only finitely many rational numbers x, y with bounded denominator and an integer m ≥ 3 satisfying the equation x(x + 1) (x + 2)…(x + (m − 1) ) = g(y). We also obtain certain finiteness results when g(y) is not an irreducible polynomial. |
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