问题及解答

Euler 的证明

\[
\frac{1}{2}\prod_{p\in PRIMES}\frac{p^2+1}{p^2-1}=\frac{\zeta^2(2)}{2\zeta(4)}=\frac{25}{20}.
\]

See [1] P.156.

References:

[1] Richard K. Guy, Unsolved Problems in Number Theory.