MathDB

N2

Part of 2022 JBMO Shortlist

Problems(1)

JBMO Shortlist 2022 N2

Source: JBMO Shortlist 2022

6/26/2023
Let a<b<c<d<ea < b < c < d < e be positive integers. Prove that 1[a,b]+1[b,c]+1[c,d]+2[d,e]≤1\frac{1}{[a, b]} + \frac{1}{[b, c]} + \frac{1}{[c, d]} + \frac{2}{[d, e]} \le 1 where [x,y][x, y] is the least common multiple of xx and yy (e.g., [6,10]=30[6, 10] = 30). When does equality hold?
number theoryLCMLowest common multipleJuniorBalkanshortlistInequality