Alright, the problem goes as follows
in mod 5, compute (a+b)^5
in mod 3 compute (a+b)^3
in mod 2 compute (a+b)^2
in mod 4 compute (a+b)^4
in mod 7 compute (a+b)^7
based on results of your findings, what do you thing (a+b)^n is equal to in mod n? Explain in detail.
Now... the a's and the b's represent classes with in the mods, and I've solved all of them out to my satisfaction except mod 4.
i have a^5 + b^5 in mod 5
a^3 + b^3 in mod 3
a^2 + b^2 in mod 2
a^7 + b^7 in mod 7
however, in mod 4, i have a^4 + 6(a^2)(b^2) + a^4
I've tried solving it out several ways, and I can't make mod 4 as pretty as the other mods. Why is this....? Am I doing the foil wrong? because I've tried it several ways to see if I was missing something, and almost thought i had it until i noticed I made a mistake and then got the result that is making it soooo not nice and neat as the others. Please help
point well taken, thanks! *chuckles* I guess i was hoping to have it nice and neat, but, I've learned long ago that its not as pretty as one would hope. But, just to make sure, if n is prime, it will be pretty right? but if its not prime.... then, each thing must be foiled out for itself, yes?
*sighs* I just wonder how my teacher wants me to put that into words.