Competition problem — Number theory

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Number theory Difficulty 6.0 National olympiad Prove it

1. Prove: For any given positive integer $K$ , there must be $K$ consecutive positive integers that are all composite.

Solution

10. $(K+1)!+2,(K+1)!+3, \cdots,(K+1)!+(K+1)$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.