Let E(x) be an arbitrary even function and n be any positive integer.
Let
H_i=\sum_{a}[E(\eta-\epsilon+i)+E(\eta-\epsilon-i)-E(\eta+\epsilon+i)-E(\eta+\epsilon-i)]
-\sum_{b}(\delta-\gamma)[E(\gamma+i)+E(\gamma-i)-E(i)-E(-i)].
where the summations goes over the partitions of n
(a) n=\eta \theta + \epsilon \zeta with \theta and \zeta odd
(b) n=\gamma \delta with \delta odd.
Given
H_0(n)+2\sum_{i=1}^{\lfloor \sqrt{n-1} \rfloor}(-1)^i H_i(n-i^2)=0.
Show that since this identity holds for all n, this implies that H_0(n)=0