8. The final proof of Kummer's criterion🔗

This chapter assembles the preceding ingredients into Kummer's criterion. The mathematical content is the equivalence p\text{ regular} \quad\Longleftrightarrow\quad \forall k,\ 1\le k,\ 2k\le p-3,\quad p\nmid (B_{2k})_{\mathrm{num}}.

1. 8.1. The minus class-number criterion
2. 8.2. The plus-to-minus divisibility step
3. 8.3. The total class number
4. 8.4. The final theorem