應用逆推網絡在克拉茲猜想的探討

Abstract

本論文主要研究一個有名的數學問題:克拉茲猜想。雖然克拉茲猜想的形式與意義容易被理解，但它仍然尚未被證明。也因為如此，引發了我們對克拉茲猜想的興趣，也希望藉著研究對它有更多的了解。首先，我們會對克拉茲猜想做個簡單的介紹，並且整理一些其他人對克拉茲猜想做的研究。接下來，我們會建構一個特別的圖，也就是逆推網絡，開始我們對克拉茲猜想的研究，同時我們也得到一些逆推網絡的特性。最後，我們嘗試建構一個模擬逆推網絡，去模擬實際的逆推網絡，根據兩者相互比較的數值結果做出分析結論。

3n+1 problem is one of the most famous conjectures in mathematics. It can be easily understood even younger children who just know how to divide by 2 and multiply by 3. However, the 3n+1 problem still can not be proved yet. Therefore, we are so interestedin this problem and hope to understand it completely. First, our study gives a brief introduction of the 3n + 1 problem, and we list some results in many research of the 3n+1 problem. Then, we use a graph, a backward iteration net, to examine the 3n+1 problem and obtain some properties in the backward iteration net. Finally, we simulate the backward iteration net and compare the numerical results with the net.