EnteredAnswer PreviewResult80021208correct2correct120At least one of the answers above is NOT correct.(1 point) This question concerns primality testing. Consider the composite number 231.Recall Fermat's Little Theorem:For any prime p and integer a, -1ap- = 1 mod p.incorrectn-1It happens that the converse to FLT is often but not always true. That is, if n is composite and a is an integer,then more often than not an #1 mod n. We can use this as the basis of a simple primality test, calledthe Fermat Test.For a Є Z231 we make the following definitions.1) We call a a Fermat Liar for n = 231 if an 11 mod n, where a € (0, 1, n − 1).n-1-2) We call a a Fermat Witness for n = 231 if a 1 mod n, where a € (0, 1, n − 1).Please answer the following.a) What is the first Fermat Liar in Z231 ?8b) What is the first Fermat Witness in Z231 ?2c) How many Fermat Liars are in Z231? Remember not to count 0,1, or n - 1.120

Answered: Image /qna-images/answer/047a0014-3676-41a9-aaeb-8f95d09fbeb1.jpg

Answered: Entered Answer Preview Result 8 00 2…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

(a) For each of the following recurrences, give an expression for theruntime T (n) if the recurrence can be solved with the Master Theorem.Otherwise, indicate that the Master Theorem does not apply.(i) T (n) = T (n/2) + T(n/2) + T(n/2) + n2(ii) T (n) = 0.5T (n/2)+ 1/n(iii) T (n) = 3T (n/3) + n(iv) T (n) = 4T (n/2) + nlogn
Python language only. Correct answer will upvoted else downvoted. Ajit understands that Omkar's timberland is a n by m lattice (1≤n,m≤2000) of some non-negative integers. Since the backwoods is honored by Omkar, it fulfills some exceptional conditions: For any two nearby (sharing a side) cells, the outright worth of the distinction of numbers in them is all things considered 1. On the off chance that the number in some cell is completely bigger than 0, it ought to be totally more prominent than the number in something like one of the cells contiguous it. Shockingly, Ajit isn't completely deserving of Omkar's forces yet. He considers each to be as a "0" or a "#". Assuming a cell is named as "0", the number in it should approach 0. Any other way, the number in it very well may be any nonnegative integer. Decide the number of various tasks of components exist to such an extent that these extraordinary conditions are fulfilled. Two tasks are considered unique if there exists…
Prove or disprove that for any x ∈ N, x(x+1)/2 ∈ N (where N = {0, 1, 2, 3, ….}
1) Direct proofs: A. Prove that for any integer x, the integer x(x + 1) is even. B. Prove that n is even if and only if n^2 is even.
Prove or disprove . show your work . (a) for any integers n a and m : if both n and m are odd, then n – m? is even (b) Vp € Z+: if p is prime, then p- 2 is not prime. (c) Vs ER : s is irrational s2 is irrational. (d) There is two odd integers n and m such that n2 – m2 – 1 is odd.
This question concerns primality testing. Recall Fermat's Little Theorem: For any prime p and integer a, aº-1 = 1 mod p. It happens that the converse to FLT is often but not always true. That is, if n is composite and a is an integer, then more often than not an #1 mod n. .n-1 We can use this as the basis of a simple primality test, called the Fermat Test. For a € Zn we make the following definitions. 'n n-1 = 1 mod n, 1) We call a a Fermat Liar for n if an where a & (0, 1, n − 1). 2) We call a a Fermat Witness for n if an−¹ ‡1 mod n, where a ‡ (0, 1, n − 1). If a number is composite, then 2 is very often a Fermat Witness. What is the smallest composite integer n greater than 4157 for which 2 is not a Fermat Witness?
Suppose we have positive integers a, b, and c, such that that a and b are not relatively prime, but c is relatively prime to both a and b . Let n = s × a + t × b be some linear combination of a and b, where s and t are integers. Prove that n cannot be a divisor of c. Follow the definition of relative primes, and use contradiction.
Let N = {0, 1, 2, . . .} be the set of Natural Numbers. Given an n ∈ N, which of the followingconditions are necessary, and which of these conditions are sufficient, for the Natural Number,n, to be a factor of 10.(a) 1 is a factor of n.(b) 1 is a factor of 2n.(c) −n is a factor of 10.(d) 10 is a multiple of n.(e) n is divisible by 2.(f) n^2 is divisible of 5.(g) n = 10.
7. For n 2 1, in how many out of the n! permutations T = (T(1), 7(2),..., 7 (n)) of the numbers {1, 2, ..., n} the value of 7(i) is either i – 1, or i, or i +1 for all 1 < i < n? Example: The permutation (21354) follows the rules while the permutation (21534) does not because 7(3) = 5. Hint: Find the answer for small n by checking all the permutations and then find the recursive formula depending on the possible values for 1(n).
6. Define the following (almost Fibonacci) recurrence for n = 0 Gn for n = 1 = Gn-1+ Gn-2+1 for n 22 Find the values of Go, G1,..., G10- Express Gn as a function of Fibonacci numbers. Prove that your expression for G, is correct for all n 2 0.
6. Prove that if m and n are integers and mn is even, then m is even or n is even.
1: Given a fixed integer B (B ≥ 2), we demonstrate that any integer N (N ≥ 0) can bewritten in a unique way in the form of the sum of p+1 terms as follows:N = a0 + a1×B + a2×B2 + … + ap×Bpwhere all ai, for 0 ≤ i ≤ p, are integer such that 0 ≤ ai ≤ B-1.The notation apap-1…a0 is called the representation of N in base B. Notice that a0 is theremainder of the Euclidean division of N by B. If Q is the quotient, a1 is the remainder of theEuclidean division of Q by B, etc.1. Write an algorithm that generates the representation of N in base B. 22. Compute the time complexity of your algorithm.

SEE MORE QUESTIONS

Recommended textbooks for you

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

C How to Program (8th Edition)

Computer Science

ISBN:

9780133976892

Author:

Paul J. Deitel, Harvey Deitel

Publisher:

PEARSON

Database Systems: Design, Implementation, & Manag…

Computer Science

ISBN:

9781337627900

Author:

Carlos Coronel, Steven Morris

Publisher:

Cengage Learning

Programmable Logic Controllers

Computer Science

ISBN:

9780073373843

Author:

Frank D. Petruzella

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS