You say "module"; do you mean "modulus"?

(I Googled "module number theory" and only came up with descriptions of courses.....

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Note: the concept of "

**modulo**" does arise, since Pythagorean triples can be characterized terms of modulii. Their lowest common denominator, as I (tried to) explain to John Gabriel some time ago.

Modulo operation (Wiki article)

Is that what you are referring to? (if so, thanks for the reminder - I had forgotten about that, and it is relevant to clarifying my proof for Fermat's theorem to number theorists, to convince them that there is a second dimension).

To the reader -------------------------------

(as noted below, I'm a little new to the concept of modulus, which is, indeed relevant to Fermat's proof and my characterization of it in terms of vectors and the relativistic unit circle; so the following definition may not be correct yet and have to be revised. I'm crunching on it. Looks like it might have something to do with computer programming. Are we SURE John Gabriel is not responding in this thread? ...

The issue is now how the concept of modulus applies to vector spaces (particularly Cartesian coordinates, but also radial coordinates), if at all (I think).........

Time will tell...

So - off the top of my head (from dim memory, long ago), and tentatively speaking for now (I'll get better):

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The division of an integer by an another (if it is a Pythagorean triple,

**mod** 0 ?

i.e.

**mod** 0 if the triple is not Pythagorean ?)

(uh, oh, there is a fraction.... warning - a second dimension may be necessary...

So

**mod** 0 if the triple is not Pythagorean?

(omg,

**another **fraction.. and there may be irrationals involved. Maybe even circles..

i.e., where what about c = a + b and

where a,b,c are integers, but not Pythagorean triples?

(Note: I was writing tex on the fly, and have deleted a number of phrases here; I will return when I finally get the tex right offline....)

Nevertheless, the plot thickens...

(I'm also a little new to the language of modulus, but it is an interesting perspective in relation to division of integers, and certainly relevant to my proof of Fermat's Theorem, particularly in reference to Lorentz rotation as an integer generator in two dimensions and the language of vectors in contrast to the single dimension integer generation (i.e., counting on a single number line) from Frege, Russell, and constructivists in general, which in turn has deep relevance to Quantum Field Theory. In the end, it will turn out that particle count cannot be conserved in two dimensions, except for relativistic Pythagorean energies (n = 2) by virtue of both the relativistic unit circle and the Binomial Theorem

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