A prime power is a number that can be written as p^i for some prime

p and some positive integer i. So, 9 = 3^ 2 is a prime power, and so is 8 = 2^ 3 . 42 = 2 · 3 · 7 is not a prime power. Prove that for any positive integer k, there exists k consecutive positive integers such that none of them are prime powers.
Hint: this is a Chinese Remainder Theorem problem

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