%Plain TeX -> abstract for V4(2) R9
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\noindent {\bf Walter Shur }
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The Last Digit of \ ${2n \choose n}$\  and\ 
 $\sum {n \choose i}{2n-2i \choose n-i}$
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Let
$f_{n}=  \sum_{i=0}^n 
 {n \choose i}{ 2n-2i\choose n-i}$,
$g_{n}=  \sum_{i=1}^n 
{n\choose i}{2n-2i \choose n-i}$.
 Let $\{a_k\}_{k=1}$ be the set of all positive 
integers n, in increasing order, for which 
${2n \choose n}$ is not divisible by 5, and 
let $\{b_k\}_{k=1}$ be the set of all positive 
integers n, in increasing order, for which $g_n$ 
is not divisible by 5. This note finds simple 
formulas for $a_k$, $b_k$,
 ${2n \choose n}$\ mod\ 10, $ f_{n}$\ mod\ 10, 
and $ g_{n}$\ mod\ 10.
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