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choose from sequence, a finite sequence with sum of terms = k

Source: Polish MO Recond Round 1978 p3

September 9, 2024
algebranumber theory

Problem Statement

Given a sequence of natural numbers (ai) (a_i) , for each natural number n n the sum of the terms of the sequence that are not greater than n n is a number not less than n n . Prove that for every natural number k k it is possible to choose from the sequence (ai) (a_i) a finite sequence with the sum of terms equal to k k .
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