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x_nx_{n+1} \le 2(x_1 + x_2 + ... + x_n) NT inequality

Source: 2013 Romania District VIII p4

September 1, 2024
number theoryinequalitiesalgebra

Problem Statement

For a given a positive integer nn, find all integers x1,x2,...,xnx_1, x_2,... , x_n subject to 0<x1<x2<...<xn<xn+10 < x_1 < x_2 < ...< x_n < x_{n+1} and xnxn+1≤2(x1+x2+...+xn).x_nx_{n+1} \le 2(x_1 + x_2 + ... + x_n).
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