Case:
2 is a primitive root of L |
Computer-assisted proof of Theorem
- Computation of Pe
- If p∉Pe, ¬(2|h-p) holds theoretically
(Proposition 5).
- If p∈Pe, ¬(2|h-p) was verified computationally
with the method of Lemma 1(II)
[computation]
- Theorem is proved. i.e. ∀p, ¬(2|h-p).
|
Computation for Proposition 2
- We see ¬(2|h-p) in all the computed cases.
- Computation: The parity of h-p was checked with the method of Lemma 1(II):
|
Case:
2 is NOT a primitive root of L |
Computation for Proposition 3
- By the following computations, we see the cases of 2|h-p are quite rare.
- 2|h-p had been known for (e,L)=(1,7) and (3,7)
- Additional exceptional 2|h-p cases, (e,L)=(3, 219−1),
(19, 7) and (29, 219−1), were found.
- Computation: The parity of h-p was checked with the method of Lemma 1(I):
|