Re: FLTAA: Field structure p = 2, p>2

From
a^n + b^n = c^n in Z we have, BWOC,
x^p + y^p = z^p in Z+ and
(z/y, z/x, x/y)^p = ( 1, 1, -1) in the multiplicative group Mx X My X
Mz.

(z/y, z/x, x/y) ^ 2p = unity in this group.

I recall a theorem from abstract algebra proposing that
Zmn is cyclic and isomorphic to
Zm X Zn if and only if gcd(m.n) = 1.

<(z/y, z/x, x/y)> are cyclic and isomorphic to Z2 X Zp if p>2.

If p = 2, then are these powers cyclic? Surely for x = 3, y= 4, z = 5,
p = 2 these powers are cyclic. What gives? That is, is there a
contradiction?

Doug Goncz
Replikon Research
Seven Corners, VA 22044-0394

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