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find (l,m,n) to form a geometric sequence

Source: China south east mathematical Olympiad 2012 day1 problem 1

July 17, 2013
geometric sequencealgebra unsolvedalgebra

Problem Statement

Find a triple (l,m,n)(l, m, n) of positive integers (1<l<m<n)(1<l<m<n), such that ∑k=1lk,∑k=l+1mk,∑k=m+1nk\sum_{k=1}^{l}k, \sum_{k=l+1}^{m}k, \sum_{k=m+1}^{n}k form a geometric sequence in order.
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