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Determine whether the following assertions are true or false. If true, prove and if false, explain or give a counterexample. 1. The integer 338 has a primitive root. 2. The ord18 (7) = 6, hence 7 is a primitive root modulo 18. 3. 7 is a quadratic residue of 107 4. x² = 3 (mod 35) has a solution. 5. The last two digits of 123403 is 21.

Determine whether the following assertions are true or false. If true, prove and if false, explain or give a counterexample. 1. The integer 338 has a primitive root. 2. The ord18 (7) = 6, hence 7 is a primitive root modulo 18. 3. 7 is a quadratic residue of 107 4. x² = 3 (mod 35) has a solution. 5. The last two digits of 123403 is 21.

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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Determine whether the following assertions are true or false. If true, prove and if false, explain or give a counterexample. 1. The integer 338 has a primitive root. 2. The ord18 (7) = 6, hence 7 is a primitive root modulo 18. 3. 7 is a quadratic residue of 107 4. x² = 3 (mod 35) has a solution. 5. The last two digits of 123403 is 21.
Transcribed Image Text:Determine whether the following assertions are true or false. If true, prove and if false, explain or give a counterexample. 1. The integer 338 has a primitive root. 2. The ord18 (7) = 6, hence 7 is a primitive root modulo 18. 3. 7 is a quadratic residue of 107 4. x² = 3 (mod 35) has a solution. 5. The last two digits of 123403 is 21.
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