Euler Function of the Catalan Numbers.

摘要

We study the solutions of the equation phi(Cm)/phi(Cn) = r where r is a xed rational number, Ck is the kth Catalan number and phi is the Euler function. We note that the number r = 4 is special for this problem and for it we construct solutions (m; n) to the above equation which are related to primes p such that 2p - 1 or 4p - 3 is also prime.