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8

Part of 1951 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1951_8

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10/8/2008
Given a positive integer n>3 n>3, prove that the least common multiple of the products x1x2⋯xk x_1x_2\cdots x_k (k≥1 k\geq 1) whose factors xi x_i are positive integers with x_1\plus{}x_2\plus{}\cdots\plus{}x_k\le n, is less than n! n!.
number theoryleast common multiplefloor functionnumber theory proposed