x^2-3x-1=0

α=(3+√13)/2,β=(3-√13)/2

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b1=(α-β)/(α-β)=1

b2=(α^2-β^2)/(α-β)=(α+β)=3

b3=3b2+b1=10

b4=3b3+b2=33

b5=3b4+b3=109

b6=3b5+b4=360

b7=3b6+b5=1189

b8=3b7+b6=3927

b9=3b8+b7=12970

b10=3b9+b8=42837

これらはマルコフ数ではない

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b1=(α+β)=3

b2=(α^2+β^2)=(α+β)^2-2αβ =11

b3=3b2+b1=36

b4=3b3+b2=119

b5=3b4+b3=393

b6=3b5+b4=1298

b7=3b6+b5=4287

b8=3b7+b6=14159

b9=3b8+b7=46764

b10=3b9+b8=154451

これらはマルコフ数ではない

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λ^2=9-4/F^2

λ^2-4=5-4/F^2

L^2-5F^2=4(-1)^n

Fがフィボナッチ数の奇数項のとき、L^2-5F^2=-4

L^2=5F^2-4

(L/F)^2=5-4/F^2・・・平方となる

ペル数の場合は

Q^2-8P^2=4(-1)^n

λ^2=9-4/P^2

λ^2-4=5-4/P^2

Pがペル数の奇数項のとき、Q^2-8P^2=-4

Q^2=8P^2-4

(Q/P)^2=8-4/P^2

λ^2=12-4/P^2でないと平方にならない

λ^2-4=8-4/P^2

P=29のときλ=√ (10088)/29

x^2-λx-1=0

x={λ+(λ^2-4)^1/2}/2

x={√ (10088)+82}/58>3???・・・おかしい

1/x=58/{√ (10088)+82}={√ (10088)-82}/58

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√5/1→x^2-x-1

√8/2→x^2-2x-1

√221/5→5x^2-11x-5

√1517/13→13x^2-29x-13

√7565/29→29x^2-63x-31・・・ペル

√10400/34→17x^2-38x-17

√71285/89→89x^2-199x-89

√257045/169→169x^2-367x-181・・・ペル

√338720/194→97x^2-216x-98・・・どちらでもない

√488597/233→233x^2-521x-233

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97x^2-216x-98=0

x={108+√ (21170)}/97+++

x=2+{-86+√ (21170)}/97

x=2+1/(97/{-86+√ (21170)})

x=2+1/({86+√ (21170)}/142)

x=2+1/(1+{-56+√ (21170)}/142)

x=2+1/(1+1/(142/{-56+√ (21170)})

x=2+1/(1+1/({56+√ (21170)}/127)

x=2+1/(1+1/(1+{-71+√ (21170)}/127)

x=2+1/(1+1/(1+1/(127/{-71+√ (21170)})

x=2+1/(1+1/(1+1/({71+√ (21170)}/127)

x=2+1/(1+1/(1+1/(1+{-56+√ (21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(127/{-56+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/({56+√ (21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+{-86+√ (21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(142/{-86+√(21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/({86+√(21170)}/97)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+{-108+√ (21170)}/97)+++

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(97/{-108+√(21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/({108+√(21170)}/98))

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+{-88+√(21170)}/98))

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(98/{-88+√(21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/{88+√ (21170)}/137)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+{-49+√ (21170)}/137)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(137/{-49+√(21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/{49+√ (21170)})/137}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+{-88+√ (21170)})/137}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(137/{-88+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/({88+√(21170)}/98)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+{-108+√(21170)}/98)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(98/{-108+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/({108+√ (21170)}/97)++++

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+{-86+√ (21170)}/97)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(97/{-86+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/({86+√(21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+{-56+√ (21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(142/{-56+√ (21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/({56+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+{-71+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(127/{-71+√(21170)}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/({71+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+{-56+√(21170)}/127)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(127/{-56+√(21170)})

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(56+√(21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+{-86+√(21170)}/142)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+1/(142/{-86+√(21170)}

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+1/({86+√(21170)}/97)

x=2+1/(1+1/(1+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(2+1/(2+1/(1+1/(1+1/(1+1/(1+1/(2+(-108+√(21170)}/97}+++

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x=[2:1,1,1,1,2,2,1,1,2---,2,1,1,1,1,2,2,1,1,2,・・・]={108+√ (21170)}/97

y={-108+√ (21170)}/97=[0:2,1,1,2,2,1,1,1,1,2,---,2,1,1,2,2,1,1,1,1,2

y=1/(2+1/(1+1/(1+1/(2+1/x)

=1/(2+1/(1+1/(1+x/(2x+1)

=1/(2+1/(1+(2x+1)/(3x+1)

=1/(2+(3x+1)/(5x+2)

=(5x+2)/(13x+5)

y=

(734+5√ (21170)/(1889+13√(21170))

(734+5√ (21170)(1889-13√(21170)))/(3568321-3577730)

(1386526-1376050-97√ (21170))/(-9409)

(-108+√ (21170))/(97)・・・OK

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