Define the following:
-
A=\sum_{n=1}^{\infty} \frac{1}{n^{6}}
-
B=\sum_{n=1}^{\infty} \frac{1}{n^{6}+1}
-
C=\sum_{n=1}^{\infty} \frac{1}{(n+1)^{6}}
-
D=\sum_{n=1}^{\infty} \frac{1}{(2 n-1)^{6}}
-
E=\sum_{n=1}^{\infty} \frac{1}{(2 n+1)^{6}}
Consider the ratios \frac{B}{A}, \frac{C}{A}, \frac{D}{A}, \frac{E}{A}. Exactly one of the four is a rational number. Let that number be r / s, where r and s are nonnegative integers and \operatorname{gcd}(r, s)=1. Concatenate r, s.
(It might be helpful to know that A=\frac{\pi^{6}}{945}.)