MathDB

6

Part of 2002 Switzerland Team Selection Test

Problems(1)

for any positive integer k exist indices i,jsuch that k =k =x_i -x_j

Source: Switzerland - Swiss TST 2002 p6

2/18/2020
A sequence x1,x2,x3,...x_1,x_2,x_3,... has the following properties: (a) 1=x1<x2<x3<...1 = x_1 < x_2 < x_3 < ... (b) xn+1≤2nx_{n+1} \le 2n for all n∈Nn \in N. Prove that for each positive integer kk there exist indices ii and jj such that k=xi−xjk =x_i -x_j.
Sequenceinequalitiesalgebra