engleski

Diophantine pairs that induce certain Diophantine triples

Diophantine tuples are sets of positive integers with the property that the product of any two elements in the set increased by the unity is a square. In this paper, it is shown that any Diophantine triple, the second largest of which is between the square and four times the square of the smallest one, is uniquely extended to a Diophantine quadruple by joining an element exceeding the largest element in the triple. As a corollary, a similar result is obtained under the hypothesis that the two smallest elements have the form $KA^2$, $4KA^4 \pm 4 A$ for some positive integers $A$ and $K \in \{;1, 2, 3, 4\};$.

Diophantine m-tuples ; Pellian equations ; linear forms in logarithms

nije evidentirano