Numbers n whose Euler Phi value Divides n + 1

Theorem
The following integers $n$ satisfy the equation:
 * $\exists k \in \Z: k \, \map \phi n = n + 1$

where $\phi$ denotes the Euler $\phi$ function:


 * $83 \, 623 \, 935, 83 \, 623 \, 935 \times 83 \, 623 \, 937$

Proof
From :
 * $\map \phi {83 \, 623 \, 935} = 41 \, 811 \, 968$

and then:

Then we have that $83 \, 623 \, 937$ is the $868 \, 421$st prime number.

From Euler Phi Function of Prime:
 * $\map \phi {83 \, 623 \, 937} = 83 \, 623 \, 936$

Then we have that:

and so: