Numbers n whose Euler Phi value Divides n + 1/Mistake/Second Edition

Source Work

 * $\mathbf B$: Divisibility
 * $\mathbf {B 37}$: Does $\map \phi n$ properly divide $n - 1$?
 * $\mathbf {B 37}$: Does $\map \phi n$ properly divide $n - 1$?

Mistake

 *  notes that $\map \phi n$ sometimes divides $n + 1$, e.g. for $n = n_1 = 3 \cdot 5 \cdot 17 \cdot 353 \cdot 929$ and $n = n_1 \cdot 83623937$. [Note that $353 = 11 \cdot 2^5 + 1, 929 = 29 \cdot 2^5 + 1, 83623937 = 11 \cdot 29 \cdot 2^{18} + 1$ and $\paren {353 - 2^8} \paren {929 - 2^8} = 2^{16} - 2^8 + 1$.]

Correction
This was in fact published by in an article in $1932$.

As this article was itself cited by in the references of this actual chapter, it is an oversight of his not to have noticed it.

In his of $2004$,  correctly attributes the result to, although still misses his final observation in an endnote of the above article:


 * ''In the same way if $6992962672132097$ is a prime
 * $3 \cdot 5 \cdot 17 \cdot 353 \cdot 929 \cdot 83623937 \cdot 6992962672132097 = 48901526933832864378258473353215$
 * is a solution of $(2)$.

continues to attribute the above to.

Also see

 * Numbers $n$ whose Euler Phi value Divides $n + 1$