Two questions about solutions of the equation
φ(x) + σ(x+1) = 3x :
If q =2^p-1 is a Mersenne prime then q is a
solution for the following equation.
σ(x+1) = 3x (*)
φ(q) = q -1 = 2^p -2 , σ(q+1) = σ(2^p)
=2^(p+1) -1 so φ(q) + σ(q+1) = 3(2^p -1) = 3q.
Q1. Is it true that, there
is no other prime solution for (*) ?
Q2. Is it true that,
Mersenne primes are the only solutions of (*) ?