3. For Gaussian integers a, plot points (2 + 3i)a on the plane. Find a complete system of representatives for Z[i]2+3i. How many are there? Is there a system of representatives consisting entirely of rational integers (in Z)? Find a system of representatives whose norms are as small as possible. 4. Recall Set #2 Exploration 3. Write out the first dozen rows of Pascal's triangle (mod 2). For example, row 5 is: [1, 1, 0, 0, 1, 1]. What patterns do you detect? For instance, which rows have all odd entries? How does row 2n compare with row n ? How many odd entries appear in row n ? Try to prove your assertions.
3. For Gaussian integers a, plot points (2 + 3i)a on the plane. Find a complete system of representatives for Z[i]2+3i. How many are there? Is there a system of representatives consisting entirely of rational integers (in Z)? Find a system of representatives whose norms are as small as possible. 4. Recall Set #2 Exploration 3. Write out the first dozen rows of Pascal's triangle (mod 2). For example, row 5 is: [1, 1, 0, 0, 1, 1]. What patterns do you detect? For instance, which rows have all odd entries? How does row 2n compare with row n ? How many odd entries appear in row n ? Try to prove your assertions.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Just answer 4!
![3. For Gaussian integers a, plot points (2 + 3i)a on the plane. Find a
complete system of representatives for Z[i]2+3i. How many are there? Is
there a system of representatives consisting entirely of rational integers (in
Z)? Find a system of representatives whose norms are as small as possible.
4. Recall Set #2 Exploration 3. Write out the first dozen rows of Pascal's
triangle (mod 2). For example, row 5 is: [1, 1, 0, 0, 1, 1]. What patterns do
you detect? For instance, which rows have all odd entries? How does row
2n compare with row n ? How many odd entries appear in row n ? Try to
prove your assertions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F882ce437-6984-48a2-b1c1-0c70a26630a5%2Fb6e4ad39-c784-47c3-be76-6f215a31dce0%2F8cylpvo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. For Gaussian integers a, plot points (2 + 3i)a on the plane. Find a
complete system of representatives for Z[i]2+3i. How many are there? Is
there a system of representatives consisting entirely of rational integers (in
Z)? Find a system of representatives whose norms are as small as possible.
4. Recall Set #2 Exploration 3. Write out the first dozen rows of Pascal's
triangle (mod 2). For example, row 5 is: [1, 1, 0, 0, 1, 1]. What patterns do
you detect? For instance, which rows have all odd entries? How does row
2n compare with row n ? How many odd entries appear in row n ? Try to
prove your assertions.
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