A362592 Discriminants D of the negative Pell equation x^2 - D*y^2 = -1, whose fundamental and all higher roots produce abc-triples a+b=c (or 1 + x^2 = D*y^2) with radical R(abc) < c.

41, 73, 89, 109, 125, 250, 338, 457, 610, 634, 761, 778, 925

Offset

1,1

Comments

It is known that fundamental and all higher roots of the corresponding positive Pell equation for these D values also produce abc-triples.

These abc-triples are rare situations for triples of additively related pairwise relatively prime positive integers a + b = c, when radical R(abc) < c. Generally R(abc) > c; see Wikipedia.

Links

Table of n, a(n) for n=1..13.

Janis Kuzmanis, On the origin of abc-triples, hal.science/hal-04044029v1.

Wikipedia, abc-conjecture.

Crossrefs

Similar sequence for discriminants of positive Pell's equation is A362591.

Sequence in context: A289982 A054806 A057540 * A105126 A214643 A142038

Adjacent sequences: A362589 A362590 A362591 * A362593 A362594 A362595

Keyword

nonn,more

Author

Janis Kuzmanis, Apr 26 2023

Status

approved