MathDB

Greater than the LCM

Source: ToT - 2001 Fall Senior A-Level #2

August 17, 2011

number theoryleast common multipleinductionnumber theory unsolved

Problem Statement

Do there exist positive integers

a_1<a_2<\ldots<a_{100}

such that for

2\le k\le100

, the least common multiple of

a_{k-1}

and

a_k

is greater than the least common multiple of

a_k

and

a_{k+1}