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Consider the congruence a² + x + 1 = 0 mod 21. Solutions to the congruence above must also be solutions to 2² + x + 1 mod (separate answers with a comma) Given the solution above, we know that all solutions to a² + x + 1 = 0 mod 21. will have the form F or mod 3 (separate answers with a comma) Solving the above system, we find that a complete solution to a² + +1 0 mod 21 is a (give least residues and separate answers with a comma) mod 7

Consider the congruence a² + x + 1 = 0 mod 21. Solutions to the congruence above must also be solutions to 2² + x + 1 mod (separate answers with a comma) Given the solution above, we know that all solutions to a² + x + 1 = 0 mod 21. will have the form F or mod 3 (separate answers with a comma) Solving the above system, we find that a complete solution to a² + +1 0 mod 21 is a (give least residues and separate answers with a comma) mod 7

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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Consider the congruence x² + x + 1 = 0 mod 21. Solutions to the congruence above must also be solutions to r² + x +1 mod (separate answers with a comma) Given the solution above, we know that all solutions to x² + x + 1 = 0 mod 21. will have the form I or mod 3. z =(separate answers with a comma) Solving the above system, we find that a complete solution to a² + x + 1 = 0 mod 21 is a =(give least residues and separate answers with a comma) mod 7
Transcribed Image Text:Consider the congruence x² + x + 1 = 0 mod 21. Solutions to the congruence above must also be solutions to r² + x +1 mod (separate answers with a comma) Given the solution above, we know that all solutions to x² + x + 1 = 0 mod 21. will have the form I or mod 3. z =(separate answers with a comma) Solving the above system, we find that a complete solution to a² + x + 1 = 0 mod 21 is a =(give least residues and separate answers with a comma) mod 7
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