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On the equation \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\). (English) Zbl 0757.11011

In the second article [for the first one, ibid. 2, No. 4, 489-510 (1991) see the review above] the authors show that the equation \[ (x+1)\dots(x+k)=(y+1)\dots (y+mk) \] with integers \(x,y\geq 0\), \(k,m\geq 2\) implies that \(\max(x,y,k)\) is bounded by an effectively computable number depending only on \(m\). In an appendix by R. Balasubramanian, some relations, not necessary for the proof, of the implied polynomials are given.
Reviewer: B.Richter (Berlin)

MSC:

11D57 Multiplicative and norm form equations
11D41 Higher degree equations; Fermat’s equation

Citations:

Zbl 0757.11010
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References:

[1] Brauer, A.; Ehrlich, G., On the irreducibility of certain polynomials, Bull. Amer. Math. Soc., 52, 844-856 (1946) · Zbl 0060.04705
[2] Chandrasekharan, K., Arithmetical functions (1970), Springer-Verlag · Zbl 0217.31602
[3] Gupta, H., Selected topics in number theory (1980), Abacus Press · Zbl 0425.10001
[4] Macmahon, Percy A., Combinatory Analysis (1960), Chelsea Publishing Company · Zbl 0101.25102
[5] Saradha, N.; Shorey, T. N., On the ratio of two blocks of conservative integers, Proc. Indian Acad. Sci. (Math. Sci.), 100, 107-132 (1990) · Zbl 0716.11017
[6] Saradha, N. and T.N. Shorey - The equations \((xxkyy mk m\); Saradha, N. and T.N. Shorey - The equations \((xxkyy mk m\) · Zbl 0757.11010
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