论文标题
套件之间的差距
Gaps between totients
论文作者
论文摘要
我们研究了正整数D的集合D，方程$ ϕ（a） - ϕ（b）= d $具有无限的许多解决方案对（a，b），其中$ ϕ $是Euler的正常函数。我们表明，D的最小为154，表现为一个特定的A，因此A中的每个倍数IS in in d in d in d in in d in in d in in d i i i i i i is a mod d具有4 | a和4 | d，其中包含无限的D。
We study the set D of positive integers d for which the equation $ϕ(a)-ϕ(b)=d$ has infinitely many solution pairs (a,b), where $ϕ$ is Euler's totient function. We show that the minumum of D is at most 154, exhibit a specific A so that every multiple of A is in D, and show that any progression a mod d with 4|a and 4|d, contains infinitely many elements of D. We also show that the Generalized Elliott-Halberstam Conjecture, as defined in [6], implies that D equals the set of all positive, even integers.
