853. Pisano Periods 1

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

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

Find the sum of the values of $n$$n$ smaller than $1000000000$$1\,000\,000\,000$ for which $\pi (n)$$\pi(n)$ equals $120$$120$.

853. 皮萨诺周期 1

对诸正整数 $n$$n$，斐波那契数列每项模 $n$$n$ 产生的新数列必是周期数列。这个周期与 $n$$n$ 有关，我们称其为 $n$$n$ 的 皮萨诺周期，常简记为 $\pi (n)$$\pi(n)$。

满足 $\pi (n)=18$$\pi(n) = 18$ 的 $n$$n$ 有 $3$$3$ 个，分别是 $19,38,76$$19, 38, 76$。这三个数中，$\le 50$$\leq 50$ 的数的和是 $57$$57$。

求所有满足 $\pi (n)=120$$\pi(n) = 120$ 且 $n\le 1000000000$$n \leq 1\,000\,000\,000$ 的 $n$$n$ 的和。

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