Naslov
A note on Diophantine quintuples

Autori
Dujella, Andrej

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Algebraic Number Theory and Diophantine Analysis : Proceedings of the International Conference / Halter-Koch, Franz ; Tichy, Robert F. - Berlin : New York : Walter de Gruyter, 2000, 123-127

ISBN
978-3-11-016304-9

Skup
International Conference : Algebraic Number Theory and Diophantine Analysis

Mjesto i datum
Graz, Austrija, 30.08.1998. - 05.09.1998

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine quintuples; elliptic curves

Sažetak
Diophantus noted that the rational numbers 1/16, 33/16, 17/4 and 105/16 have the following property: the product of any two of them increased by 1 is a square of a rational number. Let q be a rational number. A set of non-zero rationals {;a_1, a_2, ... , a_m}; is called a rational Diophantine m-tuple with the property D(q) if a_i*a_j+q is a square of a rational number for all 1 <= i < j <= m. It is easy to prove that for every rational number q there exist infinitely many distinct rational Diophantine quadruples with the property D(q). Thus we come to the following open question: For which rational numbers q there exist infinitely many distinct rational Diophantine quintuples with the property D(q)? In the present paper we give an affirmative answer to the above question for all rationals of the forms q = r^2 and q = -3r^2, r in Q.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
De Gruyter Proceedings in Mathematics

POVEZANOST RADA