The problem of the construction of Diophantine tuples,
i.e. sets with the property that product of any two of its distinct
elements is one less then a square, has a very long history.
The first Diophantine quadruple of positive rationals
was found by Diophantus himself, while the first Diophantine
quadruple of integers,
{1, 3, 8, 120},
was found by Fermat. Baker & Davenport proved that the Fermat's set
cannot be extended to a quintuple, and the famous conjecture is
that there does not exist a Diophantine quintuple in integers.
There are some new results in this area, but many open problems
and unproved conjectures still remains. I have collected the basic
information about various problems concerning Diophantine m-tuples
on the web page:
http://www.math.hr/~duje/dtuples.html
I will be very grateful on any comment or suggestion concerning
these pages. In particular, if you think that there is a paper
which should be added to the list of (more than 110) references,
please let me know.
Andrej Dujella
Department of Mathematics
University of Zagreb, CROATIA
e-mail: du...@math.hr
URL: http://www.math.hr/~duje/
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