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the lcm and prime

Source: Laurentiu Panaitopol,Romania TST 1990

August 10, 2005
number theoryleast common multiplecombinatorics proposedcombinatorics

Problem Statement

Prove that for any positive integer nn, the least common multiple of the numbers 1,2,…,n1,2,\ldots,n and the least common multiple of the numbers: (n1),(n2),…,(nn)\binom{n}{1},\binom{n}{2},\ldots,\binom{n}{n} are equal if and only if n+1n+1 is a prime number. Laurentiu Panaitopol
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