# Complete solution of a family of simultaneous Pellian equations

@inproceedings{Dujella2004CompleteSO, title={Complete solution of a family of simultaneous Pellian equations}, author={Andrej Dujella}, year={2004} }

- Published 2004

Let ck = P 2 2k + 1, where Pk denotes the k th Pell number. It is proved that for all positive integers k all solutions of the system of simultaneous Pellian equations z − ckx = ck − 1, 2z − cky = ck − 2 are given by (x, y, z) = (0,±1,±P2k). This result implies that there does not exist positive integers d > c > 2 such that the product of any two distinct elements of the set {1, 2, c, d} diminished by 1 is a perfect square. 1991 Mathematics Subject Classification: 11D09, 11D25

#### From This Paper

##### Topics from this paper.

#### Citations

##### Publications citing this paper.

Showing 1-8 of 8 extracted citations

## Nonextendibility of D(-1)-triples of the form {1, 10, c}

View 3 Excerpts

Highly Influenced

## On the extendibility of the Diophantine triple {1, 5, c}

View 3 Excerpts

Highly Influenced

## Effective Solution of the D ( − 1 )-quadruple Conjecture

View 1 Excerpt

## A parametric family of quartic Thue equations

View 1 Excerpt

## On the size of Diophantine m-tuples

View 1 Excerpt

#### References

##### Publications referenced by this paper.

Showing 1-10 of 12 references

## Simultaneous rational approximations and related diophantine equations, Math

View 4 Excerpts

Highly Influenced

## The simultaneous Diophantine equations 5y2 − 20 = x2 and 2y2 + 1 = z2

View 4 Excerpts

Highly Influenced

## Generalization of a problem of Diophantus

View 7 Excerpts

## On k-triad sequences, Internat

View 3 Excerpts

## The equations 3 x 2 − 2 = y 2 and 8 x 2 − 7 = z 2 , Quart

## The equations 3x2−2 = y2 and 8x2−7 = z2

View 3 Excerpts

## The diophantine equation y2 = ax3 +bx2 +cx+d

View 1 Excerpt