Kevin Ford, Sergei Konyagin
Published 2020-07-11Version 1
We study the set D of positive integers d for which the equation $\phi(a)-\phi(b)=d$ has infinitely many solution pairs (a,b), where $\phi$ 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.
On the Lehmer's problem involving Euler's totient function
Sparse subsets of the natural numbers and Euler's totient function
Diophantine equations involving Euler's totient function
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