MathDB
Miklos Schweitzer 1950_5

Source: second part of 1950

October 3, 2008
least common multiplenumber theory proposednumber theory

Problem Statement

Let 1≤a1<a2<⋯<am≤N 1\le a_1<a_2<\cdots<a_m\le N be a sequence of integers such that the least common multiple of any two of its elements is not greater than N N. Show that m≤2[N] m\le 2\left[\sqrt{N}\right], where [N] \left[\sqrt{N}\right] denotes the greatest integer ≤N \le \sqrt{N}
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