mersenneforum.org - View Single Post - Fermat number and Modulo for searching divisors

R.D. Silverman · 2011-05-31, 11:24

Quote:

Originally Posted by CyD

I didn't try to prove that any divisor of $2^{2^{n}}+1$ is like $X.2^{n+2}+1$ . I know it's known.
I used it in order to demonstrate the following (with the same notation than my previous message)
$2^{2^{n}-i.(m+2)} = - (-X_m)^i mod D_{m,1}$
and for example, if $2^{n} = 0 mod (m+2)$ and with $i_{max} = \frac{2^{n}}{m+2}$
then $(-X_m)^{i_{max}} = -1 mod D_{m,1}$
and if you have already prove it and if you know some internet site or book, I am interested by that.

Cyril

I will quote Serge Lang.

Your notation sucks.

I can't be bothered wading through it. If you clean it up and repost
your comments, I will take a look.

Note, however, that trivially m+2 itself is a power of 2.