September 30, 2023
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Computational Number Theory and Algebra

# NPTEL Computational Number Theory and Algebra Assignment 5 Answer

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NPTEL Computational Number Theory and Algebra Assignment 5 Answer – Here All The Questions and Answers Provided to Help All The Students and NPTEL Candidate as a Reference Purpose, It is Mandetory to Submit Your Weekly Assignment By Your Own Understand Level.

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## NPTEL Computational Number Theory and Algebra Assignment

Algebra plays an important role in both finding algorithms, and understanding the limitations of computation. This course will focus on some of the fundamental algebraic concepts that arise in computation, and the algebraic algorithms that have applications in real life. The course will cover the problems of fast integer (or polynomial) multiplication (or factoring), fast matrix multiplication, primality testing, computing discrete logarithm, error-correcting codes, lattice- based cryptography, etc. The course intends to introduce both basic concepts and practical applications.

INTENDED AUDIENCE  : Computer Science & Engineering, Mathematics, Electronics, Physics, & similar disciplines.
PREREQUISITES  : Preferable (but not necessary)– Theory of Computation, Algorithms, Algebra
INDUSTRIES  SUPPORT     : Cryptography, Coding theory, Computer Algebra, Symbolic Computing Software, Cyber Security, Learning Software

This course can have Associate in Nursing unproctored programming communication conjointly excluding the Proctored communication, please check announcement section for date and time. The programming communication can have a weightage of twenty fifth towards the ultimate score.

Final score = Assignment score + Unproctored programming exam score + Proctored Exam score
• Assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
• ( All assignments in a particular week will be counted towards final scoring – quizzes and programming assignments).
• Unproctored programming exam score = 25% of the average scores obtained as part of Unproctored programming exam – out of 100
• Proctored Exam score =50% of the proctored certification exam score out of 100
YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF ASSIGNMENT SCORE >=10/25 AND
UNPROCTORED PROGRAMMING EXAM SCORE >=10/25 AND PROCTORED EXAM SCORE >= 20/50.
If any one of the 3 criteria is not met, you will not be eligible for the certificate even if the Final score >= 40/100.

## BELOW YOU CAN GET YOUR NPTEL Computational Number Theory and Algebra Assignment 5 Answer 2022? :

1 point

x2+1×2+1 is reducible over which of the following rings?

F2[x]F2[x]

F5[x]F5[x]

GF(4)[x]GF(4)[x]

All of these

Ans – C

1 point

Let FF be a finite field of size qq and EE be some finite field extension of FF. Then, which of the following is true?

(a+b)q=aq+bq(a+b)q=aq+bq in EE, for all a,b∈Ea,b∈E.

(a+b)q=aq+bq(a+b)q=aq+bq in FF, for all a,b∈Fa,b∈F.

(a+b)q=a+b(a+b)q=a+b in FF, for all a,b∈Fa,b∈F.

All of these.

Ans –  A

1 point

Suppose there is a factorization algorithm in F[x]F[x] that computes only a single factor of the input polynomial (if it exists) in poly(d,logq)poly(d,log⁡q) time, where d is the degree of given polynomial and q is the size of finite field F. Then, which of the following is true?

There is an algorithm for irreducibility testing of polynomials in F[x]F[x] which takes poly(d,logq)poly(d,log⁡q) time.

There is a factorisation algorithm which can find all the factors of a given polynomial over F[x]F[x] and takes only poly(d,logq)poly(d,log⁡q) time.

Both of these.

None of these.

Ans –  B

1 point

Let FqFq be a finite field. Which of the following is true?

F∗qFq∗  is a cyclic group of order q.

F∗qFq∗ is a cyclic group of order q-1.

F∗qFq∗ is not a cyclic group.

None of the above.

Ans –  A

1 point

Let ff be a non-zero polynomial in Fq[x]Fq[x] where FqFq is a finite field of characteristic pp. If ∂∂x(f)=0∂∂x(f)=0 then which of the following is necessarily true?

1. ff is a constant in FqFq. 2. There exists hh in Fq[x]Fq[x] such that f=hpf=hp.

Only 1.

Only 2.

Both 1 and 2.

Neither 1 nor 2.

Ans –  B

1 point

Let ff be a square-free polynomial in Fq[x]Fq[x] where FqFq is a finite field. If we can find two polynomials gg and hh in Fq[x]Fq[x] of degrees less than the degree of ff such that g⋅h≡0modfg⋅h≡0modf, then which of the following is necessarily true?

1. gg and hh are factors of ff.
2. GCD of gg and hh with ff gives non-trivial factors of ff.

Only 1.

Only 2.

Both 1 and 2.

Neither 1 nor 2.

Ans –  B

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