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Find the least possible value of a_2000

Source: Baltic Way 2000

December 17, 2010

algebra proposedalgebra

Problem Statement

A sequence of positive integers

a_1,a_2,\ldots

is such that for each

m

and

n

the following holds: if

m

is a divisor of

n

and

m<n

, then

a_m

is a divisor of

a_n

and

a_m<a_n

. Find the least possible value of

a_{2000}

.

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