MathDB
integers uniquely determined by pairwise sums

Source: VJIMC 2001 2.1

July 26, 2021
number theorycombinatorics

Problem Statement

Let n≥2n\ge2 be an integer and let x1,x2,…,xnx_1,x_2,\ldots,x_n be real numbers. Consider N=(n2)N=\binom n2 sums xi+xjx_i+x_j, 1≤i<j≤n1\le i<j\le n, and denote them by y1,y2,…,yNy_1,y_2,\ldots,y_N (in an arbitrary order). For which nn are the numbers x1,x2,…,xnx_1,x_2,\ldots,x_n uniquely determined by the numbers y1,y2,…,yNy_1,y_2,\ldots,y_N?
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