2004
DOI: 10.4064/aa113-4-1
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The Diophantine equation x(x+1)...(x+(m-1)) + r= yn

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Cited by 10 publications
(9 citation statements)
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“…However, this equation is not symmetric like the Erdős-Selfridge equation and requires different methods. In [1], we have proved that in this case there are effective finiteness results for x, m, n ∈ Z and y ∈ Q. We shall also prove finiteness results if we delete many terms from the product involving consecutive integers.…”
Section: Erdős and Selfridgementioning
confidence: 83%
“…However, this equation is not symmetric like the Erdős-Selfridge equation and requires different methods. In [1], we have proved that in this case there are effective finiteness results for x, m, n ∈ Z and y ∈ Q. We shall also prove finiteness results if we delete many terms from the product involving consecutive integers.…”
Section: Erdős and Selfridgementioning
confidence: 83%
“…Therefore, the equation In fact, it turns out that C has degree n -4; a comparison of the coefficients ofx n-3 yields c,,-3 = 0 and that ofx n-4 is not zero. Finally, suppose we are in case (2). Then, either m = n and gl has degree 2 or m = 2n and gl is linear.…”
Section: C(x)=abm(x + (M 4-~-m + L -1)/2) ~/--M--+ L -Bfm(x)mentioning
confidence: 99%
“…In these results the extrema of polynomials played an important role. Further, we can mention papers of Beukers et al [7], Bilu et al [10], Rakaczki [33], Kulkarni and Sury [23], Bilu et al [11], Stoll and Tichy [45], Hajdu et al [21], or Bazsó et al [5] (and in fact many more), see also the survey paper of Győry et al [20] and the references there, where certain special types of separable polynomial equations were considered involving some important families of combinatorial polynomials. Also in them, the extrema of the occurring polynomials were of particular importance.…”
Section: Introductionmentioning
confidence: 99%