- Tytuł:
- On the equation $a^p + 2^α b^p + c^p = 0$
- Autorzy:
- Ribet, Kenneth
- Powiązania:
- https://bibliotekanauki.pl/articles/1390944.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- We discuss the equation $a^p + 2^α b^p + c^p = 0$ in which a, b, and c are non-zero relatively prime integers, p is an odd prime number, and α is a positive integer. The technique used to prove Fermat's Last Theorem shows that the equation has no solutions with α < 1 or b even. When α=1 and b is odd, there are the two trivial solutions (±1, ∓ 1, ±1). In 1952, Dénes conjectured that these are the only ones. Using methods of Darmon, we prove this conjecture for p≡ 1 mod 4.
- Źródło:
-
Acta Arithmetica; 1997, 79, 1; 7-16
0065-1036 - Pojawia się w:
- Acta Arithmetica
- Dostawca treści:
- Biblioteka Nauki
Artykuł