I'm having trouble proving the distributive law for [r] [s] [t] in Zn (the integers mod n)
i.e. [r]([s] + [t]) = [r][s] + [r][t]
I did this so far.
(r+m1*n)[(s+m2*n)+(t+m3*n)] = (r+m1*n)(s+m2*n)+(r+m3*n)(t+m4*n)
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*modification in red*
Now, huum... you can see, if you develop again, you have [r][s]+[r][t]
Last edited by Moo; Sep 11th 2008 at 11:17 PM.
[r] = r+mn, the m could be different for each [r], so the first [r] could have a different m than the second.
Here is an example how you prove it is well-defined.
Say you wanted to prove .
Say and .
This means and .
Thus, so .
This shows that is well-defined.
Modify this argument to the problem you have.
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