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Jun
25
awarded  Revival
Jun
23
answered proof that $1 = \sum\limits_{k=0}^n (-1)^k { 2n \choose n,k,n-k } \frac{n}{n+k}$
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16
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Jan
5
comment Proving that $f(n)=n$ if $f(n+1)>f(f(n))$
@SouvikDey: Since $f$ maps $f(k-1)$ to some value strictly smaller than $n$, the induction hypothesis applies, and so $f(f(k-1)) = f(k-1)$. (The induction hypothesis is stated in the first paragraph of Claim 3; namely, that if $f$ maps $k$ to some value $0 \leq m < n$, then the input $k$ is equal to the output $m$. The claim $f(f(k-1)) = f(k-1)$ is just saying that the input $f(k-1)$ is equal to the output $f(f(k-1))$.)
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