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Find k not satisfying divisibility condition

Source: China Second Round 2015 (A) Q4

May 5, 2016
number theorylegendre s theoremChina second round

Problem Statement

Find all positive integers kk such that for any positive integer nn, 2(k−1)n+12^{(k-1)n+1} does not divide (kn)!n!\frac{(kn)!}{n!}.
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