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For this problem, you may take for granted that 47 and 53 are prime, and that 2491 47-53. Consider the polynomial f = X²+3. Justify your answer for each part. (a) Determine whether or not the polynomial X2 +3 has a root in F47. (b) Determine whether or not the polynomial X2 + 3 has a root in F53- (c) Determine whether or not the polynomial X² + 3 has a root in Z/2491Z.

For this problem, you may take for granted that 47 and 53 are prime, and that 2491 47-53. Consider the polynomial f = X²+3. Justify your answer for each part. (a) Determine whether or not the polynomial X2 +3 has a root in F47. (b) Determine whether or not the polynomial X2 + 3 has a root in F53- (c) Determine whether or not the polynomial X² + 3 has a root in Z/2491Z.

Advanced Engineering Mathematics
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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4. For this problem, you may take for granted that 47 and 53 are prime, and that 2491 = 47.53. Consider the polynomial f = X²+3. Justify your answer for each part. (a) Determine whether or not the polynomial X² + 3 has a root in F47. (b) Determine whether or not the polynomial X2 +3 has a root in F53- (c) Determine whether or not the polynomial X² + 3 has a root in Z/2491Z.
Transcribed Image Text:4. For this problem, you may take for granted that 47 and 53 are prime, and that 2491 = 47.53. Consider the polynomial f = X²+3. Justify your answer for each part. (a) Determine whether or not the polynomial X² + 3 has a root in F47. (b) Determine whether or not the polynomial X2 +3 has a root in F53- (c) Determine whether or not the polynomial X² + 3 has a root in Z/2491Z.
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