8

Part of 1998 Korea Junior Math Olympiad

Problems(1)

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

Source: 1998 KJMO P8

T

is a set of all the positive integers of the form

2^k 3^l

k, l

are some non-negetive integers. Show that there exists

1998

different elements of

T

that satisfy the following condition.
Condition The sum of the

1998

elements is again an element of

T

setKJMOcombinatoricsExistence