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Does there Exist?

Source: ToT - 2001 Fall Junior A-Level #1

August 17, 2011

greatest common divisornumber theory unsolvednumber theory

Problem Statement

Do there exist postive integers

a_1<a_2<\cdots<a_{100}

such that for

2\le k\le100

the greatest common divisor of

a_{k-1}

and

a_k

is greater than the greatest common divisor of

a_k

and

a_{k+1}