Wednesday

August 20, 2014

August 20, 2014

Posted by **student** on Thursday, November 16, 2006 at 6:12pm.

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.

**Related Questions**

Math Help please!! - Could someone show me how to solve these problems step by ...

A number thoery question - Please help me! Thank you very much. Prove Fermat's ...

Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...

Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...

math calculus please help! - l = lim as x approaches 0 of x/(the square root of...

Math(Roots) - sqrt(24) *I don't really get this stuff.Can somebody please help ...

math,algebra,help - Directions are simplify by combining like terms. x radiacal ...

college math question - Find the GCD of 24 and 49 in the integers of Q[sqrt(3...

Math - How do you find a square root of a number that's not a perfect square? I'...

Mathematics - sqrt 6 * sqrt 8 also sqrt 7 * sqrt 5 6.92820323 and 5.916079783 So...