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Tommy groups
#1
Im very intrested in abelian gaussian Groups. I call them Tommy groups.

Beware this is not to be confused with the usual gaussian groups.
The terminology is made Up.

Basically its just the gaussian integers mod p for some prime p that satisfy Some conditions.

Or equivalent the group Z_p[i] or the ring Z mod p extended with i.

To avoid zero-divisors and make i meaningful we take p such that

X^2 = -1 mod p has no solution.
Or equivalent p =/= a^2 + b^2.

Additional conditions are considered.
And are part of the debate/theory.
Lots of number theory,ring- and group theory come together here.



X^i is a subject.
This has meaning if x^2 = -1 mod (p-1) has a solution.

Variants of fermat little and flt are also a topic.

Imho this kind of math is left too soon.
Some people say this is below their or my level , but i disagree.

Just like tetration this deserves a second look.

Thought you might wanted to know.

Regards

Tommy1729
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#2
X^{p^2}

Something to think about.

Regards

Tommy1729
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