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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.
1
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
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
KEYWORD
nonn,more
AUTHOR
Janis Kuzmanis, Apr 26 2023
STATUS
approved