Problem

Source: Indian TST 2019 Practice Test 1 P1

Tags: inequalities, india, TST, 2019, number theory



Let $a_1,a_2,\ldots, a_m$ be a set of $m$ distinct positive even numbers and $b_1,b_2,\ldots,b_n$ be a set of $n$ distinct positive odd numbers such that \[a_1+a_2+\cdots+a_m+b_1+b_2+\cdots+b_n=2019\]Prove that \[5m+12n\le 581.\]