Problem

Source: China Northern MO 2015 grade 11 p7 CNMO

Tags: number theory



Use $[x]$ to represent the greatest integer no more than a real number $x$. Let $$S_n=\left[1+\frac12 +\frac13+...+\frac{1}{n}\right], \,\, (n =1,2,..,)$$Prove that there are infinitely many $n$ such that $C_n^{S_n}$ is an even number. PS. Attached is the original wording which forgets left [ . I hope it is ok where I put it.


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