立方和问题

&nbsp; <div style="text-align:left;margin-left:0.38in;vertical-align:baseline;"> <span style="font-size:22pt;"><span>•</span></span><span style="font-family:宋体;color:black;font-size:22pt;">考虑方程式：</span><span style="font-family:Arial;color:black;font-size:22pt;">a^3 + b^3 = c^3 + d^3</span><span style="font-family:Arial;color:black;font-size:22pt;"> </span> </div> <div style="text-align:left;margin-left:0.38in;vertical-align:baseline;"> <span style="font-size:22pt;"><span>•</span></span><span style="font-family:宋体;color:black;font-size:22pt;">其中：“</span><span style="font-family:Arial;color:black;font-size:22pt;">^</span><span style="font-family:Arial;color:black;font-size:22pt;">”表示乘方。</span><span style="font-family:Arial;color:black;font-size:22pt;">a</span><span style="font-family:宋体;color:black;font-size:22pt;">、</span><span style="font-family:Arial;color:black;font-size:22pt;">b</span><span style="font-family:宋体;color:black;font-size:22pt;">、</span><span style="font-family:Arial;color:black;font-size:22pt;">c</span><span style="font-family:宋体;color:black;font-size:22pt;">、</span><span style="font-family:Arial;color:black;font-size:22pt;">d</span><span style="font-family:宋体;color:black;font-size:22pt;">是互不相同的小于</span><span style="font-family:Arial;color:black;font-size:22pt;">30</span><span style="font-family:宋体;color:black;font-size:22pt;">的正整数。</span> </div> <div style="text-align:left;margin-left:0.38in;vertical-align:baseline;"> <span style="font-size:22pt;"><span>•</span></span><span style="font-family:宋体;color:black;font-size:22pt;">这个方程有很多解。比如：</span> </div> <div style="text-align:left;margin-left:0.38in;vertical-align:baseline;"> <span style="font-size:22pt;"><span>•</span></span><span style="font-family:Arial;color:black;font-size:22pt;">a = 1</span><span style="font-family:宋体;color:black;font-size:22pt;">，</span><span style="font-family:Arial;color:black;font-size:22pt;">b=12</span><span style="font-family:宋体;color:black;font-size:22pt;">，</span><span style="font-family:Arial;color:black;font-size:22pt;">c=9</span><span style="font-family:宋体;color:black;font-size:22pt;">，</span><span style="font-family:Arial;color:black;font-size:22pt;">d=10 </span><span style="font-family:宋体;color:black;font-size:22pt;">就是一个解。因为：</span><span style="font-family:Arial;color:black;font-size:22pt;">1</span><span style="font-family:宋体;color:black;font-size:22pt;">的立方加</span><span style="font-family:Arial;color:black;font-size:22pt;">12</span><span style="font-family:宋体;color:black;font-size:22pt;">的立方等于</span><span style="font-family:Arial;color:black;font-size:22pt;">1729</span><span style="font-family:宋体;color:black;font-size:22pt;">，而</span><span style="font-family:Arial;color:black;font-size:22pt;">9</span><span style="font-family:宋体;color:black;font-size:22pt;">的立方加</span><span style="font-family:Arial;color:black;font-size:22pt;">10</span><span style="font-family:宋体;color:black;font-size:22pt;">的立方也等于</span><span style="font-family:Arial;color:black;font-size:22pt;">1729</span><span style="font-family:宋体;color:black;font-size:22pt;">。</span> </div> <div style="text-align:left;margin-left:0.38in;vertical-align:baseline;"> <span style="font-size:22pt;"><span>•</span></span><span style="font-family:宋体;color:black;font-size:22pt;">当然，</span><span style="font-family:Arial;color:black;font-size:22pt;">a=12</span><span style="font-family:宋体;color:black;font-size:22pt;">，</span><span style="font-family:Arial;color:black;font-size:22pt;">b=1</span><span style="font-family:宋体;color:black;font-size:22pt;">，</span><span style="font-family:Arial;color:black;font-size:22pt;">c=9</span><span style="font-family:宋体;color:black;font-size:22pt;">，</span><span style="font-family:Arial;color:black;font-size:22pt;">d=10 </span><span style="font-family:宋体;color:black;font-size:22pt;">显然也是解。</span> </div> <div style="text-align:left;margin-left:0.38in;vertical-align:baseline;"> <span style="font-size:22pt;"><span>•</span></span><span style="font-family:宋体;color:black;font-size:22pt;">如果不计</span><span style="font-family:Arial;color:black;font-size:22pt;">abcd</span><span style="font-family:宋体;color:black;font-size:22pt;">交换次序的情况，这算同一个解。</span> </div> <div style="text-align:left;margin-left:0.38in;vertical-align:baseline;"> <span style="font-size:22pt;"><span>•</span></span><span style="font-family:宋体;color:black;font-size:22pt;">你的任务是：找到所有小于</span><span style="font-family:Arial;color:black;font-size:22pt;">30</span><span style="font-family:宋体;color:black;font-size:22pt;">的不同的正整数解。把</span><span style="font-family:Arial;color:black;font-size:22pt;">a b c d</span><span style="font-family:宋体;color:black;font-size:22pt;">按从小到大排列，用逗号分隔，每个解占用</span><span style="font-family:Arial;color:black;font-size:22pt;">1</span><span style="font-family:宋体;color:black;font-size:22pt;">行。比如，刚才的解输出为：</span> </div> <span style="font-family:Arial;color:black;font-size:22pt;">1,9,10,12</span>