Problem 799. Pentagonal Puzzle

$P_n = \tfrac 12n(3n-1)$ giving the sequence:

1,5,12,22,35, 51,70,92,\ldots

Some pentagonal numbers can be expressed as the sum of two other pentagonal numbers. For example:

P_8 = 92 = 22 + 70 = P_4 + P_7

3577 is the smallest pentagonal number that can be expressed as the sum of two pentagonal numbers in two different ways

\begin{align} P_{49} = 3577 & = 3432 + 145 = P_{48} + P_{10} \\ & = 3290 + 287 = P_{47}+P_{14} \end{align}

107602 is the smallest pentagonal number that can be expressed as the sum of two pentagonal numbers in three different ways.

Find the smallest pentagonal number that can be expressed as the sum of two pentagonal numbers in over 100 different ways.

$P_n = \tfrac 12n(3n-1)$ ，其前几项如下：

1,5,12,22,35,51,70,92,\ldots

某些五边形数可以被拆分为两个五边形数之和，例如：

P_8 = 92 = 22 + 70 = P_4 + P_7

3577 是最小的，可以通过两种不同方法拆分成两个五边形数之和的数字。

\begin{align} P_{49} = 3577 & = 3432 + 145 = P_{48} + P_{10} \\ & = 3290 + 287 = P_{47}+P_{14} \end{align}

107602 是最小的，可以通过三种不同方法拆分成两个五边形数之和的数字。

求：最小的，可以通过一百种以上不同方法拆分成两个五边形数之和的数字。

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