hmhmhmhm,

something I made wrong. If

then n is even, then n-1 is odd, then n-1 is not divisible by 2 as needed for

.

I made the division with a ShR-order, so the last bit was ignored. A corrected form of the first conjecture is:

if and only if

is divisible by

then there is a non-negative Integer k with

mfg

Matthias