1. The following are the theorists of the 17th and 18th centuries…

/in /by

QuestionAnswered step-by-step1. The following are the theorists of the 17th and 18th centuries…1. The following are the theorists of the 17th and 18th centuries that prove theorems and made some conjectures about quadratic residues EXCEPT?* a. Fermat  b. Legendre  c. Sun Tzu  d. Euler 2. If the modulus is pn, then pkA, which is true in the following?* a. is a nonresidue modulo pn if k ? n.  b. is a nonresidue modulo pn if k < n is even.  c. is a nonresidue modulo pn if k < n is even and A is a residue.  d. is a nonresidue modulo pn if k < n is odd. 3. What theorem that was first published in the 3rd to 5th centuries by Chinese Mathematician Sun Tzu?* a. Brute-force approach  b. Algebraic approach  c. Quadratic residue theorem  d. Chinese remainder theorem 4. This article introduces the terminology "quadratic residue" and "quadratic nonresidue", and states that, if the context make it clear, the adjective "quadratic may be dropped.* a. Prime Article  b. Article 96  c. Article 95  d. Article 94 5. Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap - a is an integer multiple of p. In the notation of modular arithmetic, this is expressed as ap  ? a (mod p).* a. True  b. False 6. An approach that uses another way to find solution with basic algebra, modular arithmetic, and stepwise substitution.* a. Quadratic residues  b. Brute-force approach  c. Brute approach  d. Algebraic approach 7. Transitive theorem congruence , for all integers a, b, c, if a ? b mod n and b ? c, mod n then a ? c mod n.* a. False  b. True 8. An approach that converts congruences into sets and writes the elements out to the product. a. Quadratic residues  b. Brute-force approach  d. Algebraic approach  9. The converse of Fermat's little theorem is generally true, as it fails for Carmichael numbers. However, a slightly stronger form of theorem is not true and is known as Lehmer's theorem.* a. True  b. False 10. If the modulus is pn, then pkA, which is NOT true in the following?a. is a residue modulo pn if k ? n.* a. is a residue modulo pn if k ? n.  b. is a residue modulo pn if k < n is even and A is a residue.  c. is a nonresidue modulo pn if k < n is even and A is a residue.  d. is a nonresidue modulo pn if k < n is odd.11. The basic in composite modulus not a prime power .* a. if a is a residue modulo n, then a is a nonresidue modulo pk, for at least one prime power dividing n.  b. if a is a residue modulo n, then a is a nonresidue modulo pk, for every power dividing n.  c. if a is a nonresidue modulo n, then a is a residue modulo pk, for at least one prime power dividing n.  d. if a is a nonresidue modulo n, then a is a nonresidue modulo pk, for at least one prime power dividing n.  Option 2 12. The congruence ax ? b (mod n) has a solution if and only if b is divisible by d, where d = (a, d) .* a. True  b. Definitely true  c. False  d. None of the above 13. Whose theorem states that a natural number p > 1 is a prime number if and only if (n-1) ! ? -1 (mod n)?* a. Sun Tzu  b. Wilson  c. Fermat  d. Euler 14. Which is true about the fact that composite modulus not a prime power?* a. if a is a nonresidue modulo n, then a is a nonresidue modulo pk, for at least one every prime power dividing n.  b. if a is a nonresidue modulo n, then a is a nonresidue modulo pk, for at least one prime power dividing n.  c. if a is a nonresidue modulo n, then a is a residue modulo pk, for at least one prime power dividing n.  d. if a is a residue modulo n, then a is a nonresidue modulo pk, for every prime power dividing n. 15. If the modulus is pn, then pkA, which is true in the following?* a. a nonresidue modulo pn if k ? n.  b. a residue modulo pn if k < n is even and A is a residue.  c. a nonresidue modulo pn if k < n is even and A is a residue.  d. a nonresidue modulo pn if k < n is even. MathShare Question