3. For an odd prime p≥ 7, show that there are consecutive quadratic residues mod p, i.e., that there exists an element a € Up such that a (²) - (² + ¹) =₁ = 1. Р Hint: First show that at least one of the numbers 2, 5 and 10 is a quadratic residue mod p.
3. For an odd prime p≥ 7, show that there are consecutive quadratic residues mod p, i.e., that there exists an element a € Up such that a (²) - (² + ¹) =₁ = 1. Р Hint: First show that at least one of the numbers 2, 5 and 10 is a quadratic residue mod p.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...
Related questions
Question
[Number Theory] How do you solve question 3? The second picture is for definitions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage