- 299 名前:132人目の素数さん mailto:sage [2011/08/24(水) 07:11:40.99 ]
- >>287
(続き) [[p(n+1)], [q(n+1)]] = [[1, 1], [2, 1]][[p(n)], [q(n)]] [[p(1)], [q(1)]] = [[2], [3]] A = [[1, 1], [2, 1]]とおくと [[p(n)], [q(n)]] = A^(n-1)[2, 3] P = [[1, 1], [√2, -√2]]とおくと P^(-1) = √2/4[[√2, 1], [√2, -1]] P^(-1)AP = [[1+√2, 0], [0, 1-√2]] となるから A^(n-1) = P[[1+√2, 0], [0, 1-√2]]^(n-1)P^(-1) = √2/4[[√2((1+√2)^(n-1)+(1-√2)^(n-1)), (1+√2)^(n-1)-(1-√2)^(n-1)], [2((1+√2)^(n-1)-(1-√2)^(n-1)), √2((1+√2)^(n-1)+(1-√2)^(n-1))]] p(n) = √2/4((3 + 2√2)(1+√2)^(n-1) + (-3 + 2√2)(1-√2)^(n-1)) q(n) = √2/4((4 + 3√2)(1+√2)^(n-1) + (-4 + 3√2)(1-√2)^(n-1))
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