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Nicolae Coculescu
2004 Nicolae Coculescu
3
Fractional part Hermite-like identity
Fractional part Hermite-like identity
Source:
December 14, 2019
equations
Hermite
algebra
fractional
Floor
Problem Statement
Prove the identity
n
−
1
2
=
∑
k
=
1
n
{
m
+
k
−
1
n
}
,
\frac{n-1}{2}=\sum_{k=1}^n \left\{ \frac{m+k-1}{n} \right\} ,
2
n
−
1
=
∑
k
=
1
n
{
n
m
+
k
−
1
}
,
where
n
≥
2
,
m
n\ge 2, m
n
≥
2
,
m
are natural numbers, and
{
}
\{\}
{
}
denotes the fractional part.
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