determining x from equations of elements from field F | Mathematics | Page 1

devout fractal Jan 7, 2024, 8:56 AM

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I'm stuck after 'arriving' at the given hint

tropic moonBOT Jan 7, 2024, 8:56 AM

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half vigil Jan 7, 2024, 9:05 AM

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is it possible to just do
x²+x+1_F=0_F
(x-1_F)(x²+x+1_F)=(x-1_F)0_F
x³-1_F=0_F
?

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btw if you use the hint
x(x+1_F)=(x)(-x²)
x²+x=-x³
x²+x+1_F=-x³+1_F
.
.
etc

devout fractal Jan 7, 2024, 9:13 AM

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half vigil is it possible to just do x²+x+1_F=0_F (x-1_F)(x²+x+1_F)=(x-1_F)0_F x³-1_F=0_F ?

we haven't proven multiplication of both sides unless by multiplicative neutral 1f

half vigil Jan 7, 2024, 9:13 AM

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oh i see

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how about from the third line
x(x+1_F)=-1_F
x(-x²)=-1_F

devout fractal Jan 7, 2024, 9:23 AM

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ahh yes ill try that

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now I'm stuck here since I can't divide both sides by -

half vigil Jan 7, 2024, 9:35 AM

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can you multiply one more (-1_F) on both sides?

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not sure if that's valid with the constraints you have

devout fractal Jan 7, 2024, 9:46 AM

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I don't think so 😔

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I think this might be it 😮

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not inverse, should be mult identity

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corrected

devout fractal Jan 7, 2024, 10:14 AM

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מישהו פה?

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אין מישהו אחד שעוזר לי... למה? בבקשה!

devout fractal Jan 7, 2024, 10:33 AM

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.סגור

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.סוגר

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.close

#determining x from equations of elements from field F