Glasnik matematički, Vol. 41 No. 2, 2006.
Original scientific paper
The non-extensibility of D(4k)-triples {1, 4k(k-1), 4k^2+1} with |k| prime
Yasutsugu Fujita
Abstract
For a nonzero integer n, a set of m distinct positive integers {a1, ... , am} is called a D(n)-m-tuple if aiaj+n is a perfect square for each i, j with 1 ≤ i < j ≤ m. Let k be an integer with |k| prime. Then we show that the D(4k)-triple {1, 4k(k-1), 4k^2+1} cannot be extended to a D(4k)-quadruple.
Keywords
Simultaneous Pell equations; Diophantine tuples
Hrčak ID:
5846
URI
Publication date:
9.12.2006.
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