The number of solutions of φ (x) = m
成果类型：
Article
署名作者：
Ford, K
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.2307/121103
发表日期：
1999
页码：
283-311
关键词：
摘要：
An old conjecture of Sierpinski asserts that for every integer k greater than or equal to 2, there is a number m for which the equation phi(x) = m has exactly k solutions. Here phi is Euler's totient function. In 1961, Schinzel deduced this conjecture from his Hypothesis H. The purpose of this paper is to present an unconditional proof of Sierpinski's conjecture. The proof uses many results from sieve theory, in particular the famous theorem of Chen.