Hermite's Identity
Hermite's Identity is an identity/formula that connects floor functions to summations.
The formula is: {\displaystyle \sum _{k=0}^{n-1}\left\lfloor x+{\frac {k}{n}}\right\rfloor =\lfloor nx\rfloor .}
In this formula, ∑ is the floor function, ⌊ ⌋ is the floor function (which rounds any real number to the largest integer that is less than or equal to it), x is any real number, and n is any positive integer.
Sources: brilliant.org, Wikipedia.org, and Researchgate.net
