MathDB

18

Part of 1979 IMO Shortlist

Problems(1)

Prove that there exist fewer than 2^m such positive integers

Source:

9/15/2010
Let mm positive integers a1,…,ama_1, \dots , a_m be given. Prove that there exist fewer than 2m2^m positive integers b1,…,bnb_1, \dots , b_n such that all sums of distinct bkb_k’s are distinct and all ai (i≤m)a_i \ (i \leq m) occur among them.
number theoryAdditive Number TheoryAdditive combinatoricssystem of equationsIMO ShortlistIMO Longlist