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

Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter8: Complex Numbers And Polarcoordinates
Section8.4: Roots Of A Complex Number
Problem 41PS: Recall from the introduction to Section 8.2 that Jerome Cardans solutions to the equation x3=15x+4...
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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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