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Problem 853

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Pisano Periods 1

For every positive integer $n$ the Fibonacci sequence modulo $n$ is periodic. The period depends on the value of $n$. This period is called the Pisano period for $n$, often shortened to $\pi(n)$.

There are three values of $n$ for which $\pi(n)$ equals $18$: $19$, $38$ and $76$. The sum of those smaller than $50$ is $57$.

Find the sum of the values of $n$ smaller than $1\ 000\ 000\ 000$ for which $\pi(n)$ equals $120$.

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皮萨诺周期（一）

对任意正整数$n$，斐波那契数列对$n$取余的结果都是周期数列，其周期取决于$n$的取值。这一周期被称为$n$的皮萨诺周期，通常记为$\pi(n)$。

有三个$n$满足$\pi(n)$等于$18$，分别是$19$、$38$和$76$，其中小于$50$的两个之和为$57$。

求所有小于$1\ 000\ 000\ 000$且满足$\pi(n)$等于$120$的$n$之和。

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