another college math question

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.

  1. 👍 0
  2. 👎 0
  3. 👁 208

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Please look at my work below: Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2,

    asked by COFFEE on July 10, 2007
  2. Math/Calculus

    Solve the initial-value problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else? Thanks. y''+4y'+6y=0, y(0)=2, y'(0)=4 r^2+4r+6=0, r=(-4 +/- sqrt(16-4(1)(6))/2 r=-2 +/- sqrt(2)*i , alpha

    asked by COFFEE on July 12, 2007
  3. Calculus - Second Order Differential Equations

    Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8))

    asked by COFFEE on July 10, 2007
  4. Maath:)

    If an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h=-16t^2+vt+s (where h and s are in ft, t is in seconds and v is in ft/sec) Solve for

    asked by Honey on April 30, 2012
  5. algebra2

    If an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h=-16t^2+vt+s (where h and s are in ft, t is in seconds and v is in ft/sec) Solve for

    asked by Nancy on April 27, 2012
  6. help

    Introduction to quadratic equations? If you solve the equation by completing the square, fill in the blanks. 9x^2+9x+4=0 x^2+x+blank=-4/9+blank

    asked by Chelsea:) on April 20, 2012
  7. Algebra 2

    Introduction to quadratic equations? If you solve the equation by completing the square, fill in the blanks. 9x^2+9x+4=0 x^2+x+blank=-4/9+blank

    asked by Chelsea:) on April 24, 2012
  8. Calculus - Second Order Differential Equations

    Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2

    asked by COFFEE on July 9, 2007
  9. trig

    FInd the exact value pf the 6 trig function of alpha Given: point (-2,-6) on the terminal side of the angle in standard position sin alpha cos alpha tan alpha sec alpha csc alpha cot alpha

    asked by jacara on June 7, 2011
  10. Math:)

    A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates

    asked by girly girl on March 22, 2018

More Similar Questions