Pregled bibliografske jedinice broj: 1028477
A polynomial variant of the problem of Diophantus
A polynomial variant of the problem of Diophantus // Diophantine Analysis and Related Fields 2019 Abstracts of the talks
Tsukuba, Japan, 2019. str. 1-1 (pozvano predavanje, međunarodna recenzija, sažetak, ostalo)
CROSBI ID: 1028477 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
A polynomial variant of the problem of Diophantus
Autori
Filipin, Alan ; Jurasić, Ana
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, ostalo
Izvornik
Diophantine Analysis and Related Fields 2019 Abstracts of the talks
/ - , 2019, 1-1
Skup
Diophantine Analysis and Related Fields 2019
Mjesto i datum
Tsukuba, Japan, 07.03.2019. - 09.03.2019
Vrsta sudjelovanja
Pozvano predavanje
Vrsta recenzije
Međunarodna recenzija
Ključne riječi
Diophantine m-tuples
Sažetak
In this talk we prove that if {;a, b, c, d}; is a set of four non-zero elements of R[X], not all constant, such that the product of any two of its distinct elements increased by 1 is a square of an element of R[X], then (a+b-c-d)^2=4(ab+1)(cd+1). Some consequences of the above result are that for an arbitrary positive integer n there does not exist a set of five non-zero elements from Z[X], which are not all constant, such that the product of any two of its distinct elements increased by n is a square of an element of Z[X]. Furthermore, there can exist such a set of four non-zero elements of Z[X] if and only if n is a square. Moreover, we prove the same result for the polynomials with coefficients from the ring of Gaussian integers.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
