Y by Adventure10, Mango247
Let
. Prove that if
![\[\dfrac {1} {0^2+1}+\dfrac{1}{1^2+1}+\cdots+\dfrac{1}{(p-1)^2+1}=\dfrac{m} {n},\]](//latex.artofproblemsolving.com/d/5/f/d5f55cc86a95d51109ace2dc3e737bddecc144b0.png)
where we only sum over terms with denominators not divisible by
(and the fraction
is in reduced terms) then
.
Proposed by A. Golovanov

![\[\dfrac {1} {0^2+1}+\dfrac{1}{1^2+1}+\cdots+\dfrac{1}{(p-1)^2+1}=\dfrac{m} {n},\]](http://latex.artofproblemsolving.com/d/5/f/d5f55cc86a95d51109ace2dc3e737bddecc144b0.png)
where we only sum over terms with denominators not divisible by



Proposed by A. Golovanov