- Hello all!

Can anyone give me a reference(if possible on the web) of the

following theorem:

Let p be prime, d=2*p*j+1, d=1(mod 8) and j even, then

x^{2j}=2 (mod d) is solvable if and only if 2^p=2^{(d-1)/(2j)}=1 (mod d)

Thanks a lot - Let p=3, j=8, so d=49.

x=16 and 33 solve x^16=2 mod 49

2^3 mod 49 is obviously not 1

Adam

--- In primenumbers@yahoogroups.com, "najibaamimar"

<najibaamimar@...> wrote:>

(mod d)

> Hello all!

>

> Can anyone give me a reference(if possible on the web) of the

> following theorem:

> Let p be prime, d=2*p*j+1, d=1(mod 8) and j even, then

> x^{2j}=2 (mod d) is solvable if and only if 2^p=2^{(d-1)/(2j)}=1

>

> Thanks a lot

>