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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29x^2-63x-31=0

x={63+√ (7565)}/58++

x=2+{-53+√ (7565)}/58

x=2+1/(58/{-53+√ (7565)})

x=2+1/({53+√ (7565)}/82)

x=2+1/(1+{-29+√ (7565)}/82)

x=2+1/(1+1/(82/{-29+√ (7565)})

x=2+1/(1+1/({29+√ (7565)}/82)

x=2+1/(1+1/(1+{-53+√ (7565)}/82)

x=2+1/(1+1/(1+1/(82/{-53+√ (7565)})

x=2+1/(1+1/(1+1/({53+√ (7565)}/58)

x=2+1/(1+1/(1+1/(2+{-63+√ (7565)}/58)+++

x=2+1/(1+1/(1+1/(2+1/(58/{-63+√ (7565)})

x=2+1/(1+1/(1+1/(2+1/({63+√ (7565)}/62)

x=2+1/(1+1/(1+1/(2+1/(2+{-61+√ (7565)}/62)

x=2+1/(1+1/(1+1/(2+1/(2+1/(62/{-61+√ (7565)})

x=2+1/(1+1/(1+1/(2+1/(2+1/({61+√ (7565)}/62)

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+{-63+√ (7565)}/62)

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(62/{-63+√ (7565)})

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/({63+√ (7565)}/58))+++

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+{-53+√ (7565)}/58))

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(58/{-53+√ (7565)})

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/{53+√ (7565)}/82)

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(1+{-29+√ (7565)}/82)

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(1+1/(82/{-29+√ (7565)})

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(1+1/{29+√ (7565)})/82

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(1+1/(1+(-53+√ (7565)})/82)）

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(1+1/(1+1/(82/{-53+√ (7565)})

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(1+1/(1+1/({53+√ (7565)}/58)

x=2+1/(1+1/(1+1/(2+1/(2+1/(2+1/(2+1/(1+1/(1+1/(2+{-63+√ (7565)}/58)+++

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x=[2:1,1,2,2,2,--2,1,1,2,2,2,--2,1,・・・]={63+√ (7565)}/58

y={-63+√ (7565)}/58=[0:2,2,2,1,1,2,---2,2,2,1,1,2]

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

y=

(184+2√ (7565))/(431+5√ (7565))

(184+2√ (7565))(431-5√ (7565))/(185761-189125)

(79304-75650-58√ (7565))/(-3364)

(3654-58√ (7565))/(-3364)=(-63+√ (7565))/(58)・・・OK

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