A362591 - OEIS

A362591

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

%I #29 Nov 13 2023 07:31:56

%S 2,5,7,8,12,13,14,18,20,21,27,28,29,31,32,39,41,45,46,47,48,50,52,53,

%T 54,56,60,62,63,67,69,70,72,73,74,75,77,79,80,84,85,89,92,93,96,98,

%U 103,108,109,112,113,114,116,117,122,124,125,126,127,128,135,137,139,145,147,149,150

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

%C 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.

%H Janis Kuzmanis, <a href="/A362591/b362591.txt">Table of n, a(n) for n = 1..390</a>

%H Janis Kuzmanis, <a href="https://hal.science/hal-04044029v1">On the origin of abc-triples</a>, hal.science/hal-04044029v1.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Abc_conjecture">abc-conjecture</a>.

%Y Similar sequence for the negative Pell's equation is A362592.

%K nonn

%O 1,1

%A _Janis Kuzmanis_, Apr 26 2023

%E More terms from _Janis Kuzmanis_, Nov 12 2023