MathDB
Find sequences of reals with two sums

Source: Polish Second Round 2009

August 4, 2011
vectorlinear algebraalgebra unsolvedalgebra

Problem Statement

For every integer n≥3n\ge 3 find all sequences of real numbers (x1,x2,…,xn)(x_1,x_2,\ldots ,x_n) such that ∑i=1nxi=n\sum_{i=1}^{n}x_i=n and ∑i=1n(xi−1−xi+xi+1)2=n\sum_{i=1}^{n} (x_{i-1}-x_i+x_{i+1})^2=n, where x0=xnx_0=x_n and xn+1=x1x_{n+1}=x_1.
Back to ProblemsView on AoPS