Hi, I am having problem with solving this task from my math homework. If number p is prime and p^2+8 is also prime. Prove that p^3+4 is also prime number.
Пожалуйста, подпишитесь на официальный канал Codeforces в Telegram по ссылке https://t.me/codeforces_official.
→ Обратите внимание
→ Трансляции
→ Лидеры (рейтинг)
| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | tourist | 3880 |
| 2 | jiangly | 3669 |
| 3 | ecnerwala | 3654 |
| 4 | Benq | 3627 |
| 5 | orzdevinwang | 3612 |
| 6 | Geothermal | 3569 |
| 6 | cnnfls_csy | 3569 |
| 8 | jqdai0815 | 3532 |
| 9 | Radewoosh | 3522 |
| 10 | gyh20 | 3447 |
| Страны | Города | Организации | Всё → |
→ Лидеры (вклад)
| № | Пользователь | Вклад |
|---|---|---|
| 1 | awoo | 161 |
| 2 | maomao90 | 160 |
| 3 | adamant | 156 |
| 4 | maroonrk | 153 |
| 5 | -is-this-fft- | 148 |
| 5 | atcoder_official | 148 |
| 5 | SecondThread | 148 |
| 8 | Petr | 147 |
| 9 | nor | 144 |
| 9 | TheScrasse | 144 |
→ Найти пользователя
→ Прямой эфир
Codeforces (c) Copyright 2010-2024 Михаил Мирзаянов
Соревнования по программированию 2.0
Время на сервере: 22.07.2024 02:21:43 (h1).
Десктопная версия, переключиться на мобильную.
При поддержке
Suppose that p ≠ 3. Then
thus p2 + 8 is not prime and we were wrong in our assumption. Then p = 3 and p3 + 4 = 31 which is obviously prime.
How to prove that p2 = 1 mod 3?
Fermat's little theorem. If p is prime, then
This is a special case of Euler's theorem, which is formulated like this for coprime a, m:
