1947/01/01 by Victor Klee · 30 citations
Computer Science · Mathematics · #semigroups and automata theory #Conjecture #Euler's totient function #Mathematics #Combinatorics #Integer (computer science) #Euler's formula #Set (abstract data type) #Discrete mathematics #Upper and lower bounds #Mathematical analysis #Computer science
paper · pdf · doi:10.1090/s0002-9904-1947-08940-0
published in Bulletin of the American Mathematical Society 53(12), 1183-1186 (American Mathematical Society)
openalex publication_date 1947/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
V. L. KLEE, JR. 1 Carmichael [ l ] 2 conjectured that for no integer n can the equation (x)=n ( being Euler's totient) have exactly one solution. To support the conjecture, he showed that each n for which there is a unique solution must satisfy a restriction which implies w>10. In this note we prove the validity of restrictions considerably stronger than those of Carmichael, and raise the lower bound on n to 10. We shall denote by X the set of all integers x for which (y)=<l)(x) implies y = x. (If the conjecture is correct, X is empty, and the theorems stated are vacuously satisfied.)