another college math question
posted by student .
Please teach me. I am completely blank with it. :(
Let alpha = (3+sqrt(3))/2 belongs to Q[sqrt(3)].
Show that if x is congruent to 1 mod alpha, then x^3 is congruent to 1
(mod alpha)^3.
Similarly, show that if x is congruent to 1 mod alpha, then x^3 is congruent to
1 (mod alpha)^3 , and that if x is congruent to 0 mod alpha, then x^3 is congruent to 0 (mod alpha)^3.
Hint: you can factor x^3 1 in Q[sqrt(d)] completely into linear factors.
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