Problem 348
Sum of a square and a cube
Many numbers can be expressed as the sum of a square and a cube. Some of them in more than one way.
Consider the palindromic numbers that can be expressed as the sum of a square and a cube, both greater than 1, in exactly 4 different ways.
For example, 5229225 is a palindromic number and it can be expressed in exactly 4 different ways:
22852 + 203
22232 + 663
18102 + 1253
11972 + 1563
Find the sum of the five smallest such palindromic numbers.
平方数和立方数之和
许多数可以表示称一个平方数和一个立方数之和，有些数甚至有不止一种表示方式。
考虑能表示成大于1的平方数和立方数之和，且恰好有4种不同的表示方式的回文数。
例如，5229225是一个回文数，而且它恰好可以用4种不同的方式进行表达：
22852 + 203
22232 + 663
18102 + 1253
11972 + 1563
求出这类回文数中最小的五个之和。