Linear Equations with the Euler Totient Function.

摘要

In this paper, we investigate linear relations among the Euler function of nearby integers. In particular, we study those positive integers n such that theta(n) = theta(n -1) + (n - 2), where theta is the Euler function. We prove that they form a set of asymptotic density zero. We also show that the sum of the reciprocals of the prime values of n with the above property is a convergent series.