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ASU 459 All Soviet Union MO 1987 T_0 set consists of all (2k)!

Source:

August 7, 2019

setnumber theorycombinatorics

Problem Statement

The

T_0

set consists of all the numbers, representable as

(2k)!, k = 0, 1, 2, ... , n, ...

. The

T_m

set is obtained from

T_{m-1}

by adding all the finite sums of different numbers, that belong to

T_{m-1}

. Prove that there is a natural number, that doesn't belong to

T_{1987}