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CSMO Grade 10 Problem 7

Source: CSMO Grade 10 Problem 7

August 6, 2017

number theoryIntegers

Problem Statement

Let

m

be a given positive integer. Define

a_k=\frac{(2km)!}{3^{(k-1)m}},k=1,2,\cdots.

Prove that there are infinite many integers and infinite many non-integers in the sequence

\{a_k\}