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Let D be a squarefree integer, and let 0 be the ring of integers in the quadratic field Q(√D). For any positive integer f prove that the set Of = Z[fw] = {a + bfw | a, b E Z} is a subring of 0 containing the identity. Prove that [O:Of]= f (index as additive abelian groups). Prove conversely that a subring of 0 containing the identity and having finite index f in 0 (as additive abelian group) is equal to Of. (The ring Of is called the order of conductor f in the field Q(√D). The ring of integers 0 is called the maximal order in Q(√D).
Does the use of linear algebra make this method easier to understand or use?
Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold then how many of each were sold?
what is the algebraic expression for the following word phrase
Suppose Bob owns 8000 shares of company X and 6000 shares of Company Y. The total value of Bobs holding of these 2 companies is $680,000.
Suppose the Phillips curve is represented by the following: πt = πte + 0.20 - 2ut where πte = θπt=1. Assume θ = 0.8, πt=1 = 0.10 (10%) and ut = 0.05 (5%). Calculate πt.
Which sum will be irrational
Solving the equation algebraically
Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen
A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do you have?" How many gold coins does the rich merchant have?
find a polynomial of degree 5 with real coefficients and i as a root of multiplicity 2 and the square root of 5 as a
A cube, painted green on the outside and measuring 15 centimeters on each edge, is cut into congruent cubes measuring 5 centimeters on each edge.
Discuss the general shape and location of each of your graphs - State the domain and range for each of your equations. Write them in interval notation and state whether each of the equations is a function or not giving your reasons for the answer.
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