Quote:
Originally Posted by paulunderwood
I don't see why it has to be base 2 Fermat PRP; The norm is 1.

By "your condition" I mean, any of Mod(Mod(1,n) + x, x^4 + 1)^n == Mod(1 + x^r, x^4 + 1) for n == r (mod 8), r =3, 5, or 7.
Any of these conditions imply that Mod(2,n)^n = Mod(2,n).
My "reduced" condition does NOT imply that Mod(2,n)^n = Mod(2,n) (see example next paragraph). It only covers part of the test for n == 5 (mod 8). It merely insures that in Mod(Mod(1,n) + x, x^4 + 1)^n, the coefficients of x^3 and x^2 are 0.
A mindless numerical sweep found that 1189 = 29*41 is
not a 2psp but
does satisfy my "reduced" condition.
I note that 341, a 2psp congruent to 5 (mod 8), does
not satisfy my "reduced" condition.
So combining 2psp with my "reduced" condition may work fairly well for n == 5 (mod 8), but I suspect there are 2psp's congruent to 5 (mod 8) which satisfy my "reduced" condition, but
not your condition
Mod(Mod(1,n) + x, x^4 + 1) = Mod(Mod(1,n)  x, x^4 + 1).