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The problem of Diophantus for integers of Q(√−3)

Zrinka Franušić orcid id orcid.org/0000-0003-3481-8057 ; Department of Mathematics, University of Zagreb, Bijenička cesta 30, HR-10 000 Zagreb, Croatia
Ivan Soldo orcid id orcid.org/0000-0002-6195-6626 ; Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31 000 Osijek, Croatia


Puni tekst: engleski pdf 199 Kb

str. 15-25

preuzimanja: 573

citiraj


Sažetak

We solve the problem of Diophantus for integers of the
quadratic field Q(√−3) by finding a D(z)-quadruple in Z[(1+√−3)/2] for
each z that can be represented as a difference of two squares of integers in Q(√−3), up to finitely many possible exceptions.

Ključne riječi

Diophantine quadruples, quadratic field

Hrčak ID:

127639

URI

https://hrcak.srce.hr/127639

Posjeta: 1.117 *