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a_1!a_2! ... a_n! < k! where k > sum a_i

Source: Eotvos 1937 p1

September 10, 2024
algebrainequalities

Problem Statement

Let nn be a positive integer. Prove that a1!a2!...an!<k!a_1!a_2! ... a_n! < k!, where kk is an integer which is greater than the sum of the positive integers a1,a2,..,ana_1, a_2,.., a_n.
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