The first of an infinite triangular spreadsheet the line contains one number, the second line contains two numbers, the third line contains three numbers, and so on. In doing so is in any k-th row (k=1,2,3,...) in the first and last place the number k, each other the number in the table is found, however, than in the previous row the least common of the two numbers above it multiple (the adjacent figure shows the first five rows of this table). We choose any two numbers from the table that are not in their row in the first or last place. Prove that one of the selected numbers is divisible by another.
Problem
Source: 2000 Estonia National Olympiad Final Round grade 12 p2
Tags: Pascal's Triangle, LCM, divides, number theory, divisible