Download PTU B.Sc CS-IT 2020 March 4th Sem 72317 Number Theory Question Paper

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Roll No. Total No. of Pages : 02
Total No. of Questions : 07

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B.Sc.(Computer Science) (2013 & Onwards) (Sem.-4)
NUMBER THEORY
Subject Code : BCS-401
M.Code : 72317
Time : 3 Hrs. Max. Marks : 60

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have to attempt any FOUR questions.

SECTION-A

1. Answer the followings in short :
   1. Find G.C.D. 0f (49,210,350).

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   2. Show that n is odd iff n = I(mod2).
   3. Give an example to show that if ab’= 0(mod m), then a# 0(mod m) and b= 0 (mod m)
   4. Solve the linear congruence-:9x = 21(mod 30).
   5. State Euclidean algorithm.
   6. State Euler’s theorem.

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   7. State Wilson’s theorem.
   8. Define Euler phi function.
   9. Calculate the value of ¢ (360).
   10. For n> 2, ¢ (n) is an even integer.

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SECTION-B

2. Prove that the numbers of primes are infinite.
3. Find values of x and y to satisfy 71x — 50y = 1.
4. State and prove Fundamental theorem of Arithmetic.
5. State and prove Chinese remainder theorem.

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6. State and prove Mobius inversion formula.
7. State and prove Fermat’s theorem.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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