I would like to understand the math behind this...
Simply and objectively!In decimal for ease.
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Private key : 1
Public key :
x = 55066263022277343669578718895168534326250603453777594175500187360389116729240
55066263022277343669578718895168534326250603453777594175500187360389116729240**3 + 7 =
32748224938747404814623910738487752935528512903530129802856995983256684603122**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 32670510020758816978083085130507043184471273380659243275938904335757337482424
OKAY
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Private key : 2
Public key :
x = 89565891926547004231252920425935692360644145829622209833684329913297188986597
89565891926547004231252920425935692360644145829622209833684329913297188986597**3 + 7 =
57199941671890039290383617934355424684258807805258215939368959893591666662646**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 12158399299693830322967808612713398636155367887041628176798871954788371653930
OKAY
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Private key : 3
Public key :
x = 112711660439710606056748659173929673102114977341539408544630613555209775888121
112711660439710606056748659173929673102114977341539408544630613555209775888121**3 + 7 =
104193826873522593991639737736096919049125888873761064059040146529970392609905**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 90209061256745311731914079131285931446821116410824268969537695047367247992253
NO OKAY
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Why doesn't private key 3 meet the criteria of the previous ones?
What math or method is used to define when you need to use -y?