Naslov
There does not exist a D(4)-sextuple

Autori
Filipin, Alan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
25th Journees Arithmetiques / Cremona, John ; Greaves, George ; Smyth, Chris - Edinburgh : University of Edinburgh, 2007, 14-14

Skup
25th Journees Arithmetiques

Mjesto i datum
Edinburgh, Ujedinjeno Kraljevstvo, 02.07.2007. - 06.07.2007

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Pellian equations

Sažetak
A set of m positive integers is called a D(4)-m-tuple, if the product of any two of its distinct elements increased by 4 is a perfect square. There is a conjecture that D(4)-triple {; ; ; a, b, c}; ; ; can be extended to a D(4)-quadruple{; ; ; a, b, c, d}; ; ; such that d > max{; ; ; a, b, c}; ; ; in the unique way. That was proved for D(4)-triple {; ; ; 1, 5, 12}; ; ; and various parametric families of D(4)-triples. We prove that there does not exist a D(4)-sextuple.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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