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Questions in category: 初等数论 (Elementary Number Theory).

Euler

Posted by haifeng on 2025-01-01 11:58:33 last update 2025-01-01 14:32:43 | Answers (0) | 收藏


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.