This is definition of dedekind sums : https://mathworld.wolfram.com/DedekindSum.html
Let {u(n)} be fibonacci sequence such that u(1)=u(2)=1 and u(n+1) = u(n)+u(n-1). If h=u(2n) and k=u(2n+1) then prove that s(h,k)=0.
according to defination of s(h,k) i simplified s(h,k) but I am having problem in how to simplify $\sum_{r=1}^{u(2n+1)-1} [ \frac{u(2n) r} {u(2n+1)}]$. Here [ ] is greatest integer function. Rest of summatiuons I have simplified the rest but in this I am not sure what property of fibonacci sequence should ve used.
Thaks for any help