论文标题
Erdos-Straus猜想的溶液的结构和形式
Structure and form of the solutions of the Erdos-Straus conjecture
论文作者
论文摘要
在本文中，我们将满足Erdos-Straus猜想的P的某些值分类，即形式4/N的分数分解为三个分数的总和，分子相同等于1，而不是根据它们的模块化相似性，而是根据它们具有相同结构的解决方案的事实。我们对满足其形式的所有解决方案进行了分类（DU，DV，DUV），并找到最初难以分类的P值的特征，例如P = 1009。我们还研究了满足GCD（X，Y，Z）= X的解决方案（X，Y，Z），最后，我们将这两个变量中的任何一个彼此重合的所有情况进行了分类。
In this paper we classify certain values of p that satisfy the Erdos-Straus conjecture, concerning the decomposition of fractions of the form 4/n as sum of three fractions with numerator identically equal to 1, not according to their modular similarity but to the fact that they share solutions with identical structure. We classify all solutions that satisfy that they are of the form (du,dv,duv) and find characterizations for values of p that were initially difficult to classify, such as p=1009. We also study the solutions (x,y,z) that satisfy that gcd(x,y,z)=x and, finally, we classify all the cases in which any of these two variables coincide with each other.
