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1998 KJMO P8 Existence of 1998 elements in a set(T)

Source: 1998 KJMO P8

June 30, 2024
setKJMOcombinatoricsExistence

Problem Statement

TT is a set of all the positive integers of the form 2k3l2^k 3^l, where k,lk, l are some non-negetive integers. Show that there exists 19981998 different elements of TT that satisfy the following condition.
Condition The sum of the 19981998 elements is again an element of TT.
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