MathDB

2

Part of 1980 Austrian-Polish Competition

Problems(1)

every positive integer k can be written as x_j -x_i for some i, j if x_{n+1}<=2n

Source: Austrian Polish 1980 APMC

4/26/2020
A sequence of integers 1=x1<x2<x3<...1 = x_1 < x_2 < x_3 <... satisfies xn+1≤2nx_{n+1} \le 2n for all nn. Show that every positive integer kk can be written as xj−xix_j -x_i for some i,ji, j.
Sequenceinequalitiesnumber theory