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Perfect Powers that are Sums of Consecutive like Powers

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Vandita Patel
University of Warwick/MPI
Wed, 2017-05-10 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

In this talk, we present some of the techniques used to tackle subfamilies of the Diophantine equation
(x+1)^k + (x+2)^k + ... + (x+d)^k = y^n. We compare two very different approaches which naturally
arise when considering the parity of k. We present all integer solutions, (x,y,n) to the equation in the
case k=3, 1<d<51 (joint work with Mike Bennett - UBC and Samir Siksek - Warwick), and a (natural)
density result when k is a positive even integer, showing that for almost all d at least 2, the equation
has no integer solutions, (x,y,n) with n at least 2(joint work with Samir Siksek - Warwick).

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