Hermite's Identity

Hermite's Identity (named after Charles Hermite) is an identity/formula that connects floor functions to summations.

The formula is: ∑ (from k=0 to n-1) ⌊x + k/n⌋ = ⌊nx⌋

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

       -Evzen