Fantaisie

回学校一周。

时差上个周末终于倒了过来，感慨为什么这次的反应这么强烈，刚到得时候头晕了整两天，难道未老先衰了？最后还是无奈中去体育馆猛运动了一番，才算是甩掉了那头晕。。。

暑期的数学研究已渐渐步入正轨，今天上午和导师讨论的时候提出了第一个conjecture，说是虽然6和12的倍数的abundancy index比较高，但是如果把两个相邻的数字相乘，他们乘积的abundancy index总体来说会甚至更高。明天上午还要再讨论，今天忙了一晚上算是又发现一些新现象供明天讨论，反正这个星期的主要任务就是观察总结规律然后提出待证明的假设。这课题挺有意思的，可是这两天在那里数那些数字然后fit them with quadratic formulas已经有点头晕眼花了，不过还是看到了不少曙光，所以还是得坚持的。

下面是导师关于这个课题的介绍论文的摘要：
Some of the oldest open problems in mathematics relate to the abundancy index of a number.  Are there infinitely many perfect numbers?  Does there exist an odd perfect number?  Does there exist an odd multiply perfect number?  Such questions have been considered for well over two millennia by the likes of Euclid, Fermat, Descartes, Mersenne, Legendre, and Euler. Yet the answers to these questions still elude us.  In this paper, we examine the abundancy indexes of positive integers in a visual way, by assigning a color to each positive integer based on the value of its abundancy index. In this way, we will be able to see abundancy patterns within the set of integers.  Such visualizations are not only eye-catching, but also helpful in understanding the nature of the integers themselves.

还有两个月的时间，希望我们能做出一些小成果：D