地方競馬全国協会（ちほうけいばぜんこくきょうかい、英称：National Association of Racing）は、競馬法に基づく地方共同法人である。略称は英語の頭文字からNAR、あるいは地全協。地方公共団体によって主催される地方競馬の公正かつ円滑な実施の推進を図るとともに、馬の改良増殖その他畜産の振興に資することを目的とする（競馬法第23条の10）。
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edited Jul 31 '12 at 14:45
Jorge Castro
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asked Jul 31 '12 at 5:16
Goivind Tiwari Goivind Tiwari
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I have found the following Fibonacci Identity (and proved it). If $F_n$ denotes the nth Fibonacci Number, we have the following identity begin{equation} F_{n-r+h}F_{n+k+g+1} - F_{n-r+g}F_{n+k+h+1} = (-1)^{n+r+h+1} F_{g-h}F_{k+r+1} end{equation} where $F_1 = F_2 = 1$ , $r leq n$ , $h leq g$ , and $n, g, k in mathbb{N}$ . It is not too hard to show that this identity subsumes Cassini's Identity, Catalan's Identity, Vajda's Idenity, and d'Ocagne's identity to name a few. I have done a pretty thorough literature review, and I have not found anything like this, but I am still wondering if anyone has seen this identity before? I found this by accident after noticing some patterns in some analysis work I was doing, so if this is already known I would be curious to see w...
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