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問題
- 1000-digit Fibonacci number
私訳
- 1000桁のフィボナッチ数
解答方針

問題

1000-digit Fibonacci number

The Fibonacci sequence is defined by the recurrence relation:

$F_n = F_{n−1} + F_{n−2}$ , where $F_1 = 1$ and $F_2 = 1$ . Hence the first 12 terms will be:

$F_1 = 1$

$F_2 = 1$

$F_3 = 2$

$F_4 = 3$

$F_5 = 5$

$F_6 = 8$

$F_7 = 13$

$F_8 = 21$

$F_9 = 34$

$F_{10} = 55$

$F_{11} = 89$

$F_{12} = 144$

The 12th term, $F_{12}$ , is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?