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WITH RECURSIVE
triplets AS
(
SELECT a::numeric, b::numeric, c::numeric
FROM generate_series( 1, 30 ) a
, generate_series( 1, 30 ) b
, generate_series( 1, 30 ) c
ORDER BY a, b, c
)
, cardano_sum AS
(
SELECT a, b, c,
( a + b * sqrt( c ) ) AS l
,( a - b * sqrt( c ) ) AS r
FROM triplets
)
, cardano AS
(
SELECT a, b, c, l, r
, CASE WHEN l < 0 THEN -1 ELSE 1 END * pow( abs( l )::numeric, 1/3::numeric )
+ CASE WHEN r < 0 THEN -1 ELSE 1 END * pow( abs( r )::numeric, 1/3::numeric )
AS triplet_sum
FROM cardano_sum
)
SELECT *
FROM cardano
WHERE
abs( 1 - triplet_sum::numeric ) <= 0.0000000001
LIMIT 5
;
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