On the wikipedia, near the bottom of the "Specific Values" section, there is a statement that bothers me.
$$\zeta(-13)=\zeta(-1)$$
Firstly, it is well noted that the summations must be evaluated somehow, despite the fact that they are divergent.
Secondly, it just seemed very random, without much reinforcement, so I feel as though it could be a typo or foul play.
Hopefully the latter is false and someone can shed some light on proving they are equal.
It turns out to be an identity about Bernoulli numbers, $B_2=B_{14}-1$. They both are rational numbers, and their denominators have to be the same by the Von Staudt-Clausen theorem. Equality of numerators, too, happens more or less by chance.