MathDB
Putnam 2003 B3

Source:

June 23, 2011
Putnamnumber theoryleast common multiplefloor functionprime factorizationcollege contests

Problem Statement

Show that for each positive integer n, n!=∏i=1n  lcm  {1,2,…,⌊ni⌋}n!=\prod_{i=1}^n \; \text{lcm} \; \{1, 2, \ldots, \left\lfloor\frac{n}{i} \right\rfloor\} (Here lcm denotes the least common multiple, and ⌊x⌋\lfloor x\rfloor denotes the greatest integer ≤x\le x.)
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