MathDB
Integer inequality

Source: Indian TST 2019 Practice Test 1 P1

July 17, 2019
inequalitiesindiaTST2019number theory

Problem Statement

Let a1,a2,…,ama_1,a_2,\ldots, a_m be a set of mm distinct positive even numbers and b1,b2,…,bnb_1,b_2,\ldots,b_n be a set of nn distinct positive odd numbers such that a1+a2+⋯+am+b1+b2+⋯+bn=2019a_1+a_2+\cdots+a_m+b_1+b_2+\cdots+b_n=2019 Prove that 5m+12n≤581.5m+12n\le 581.
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