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

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B-Sc CSE-IT (Bachelor of Science in Computer Science) 2020 March 4th Sem 72317 Number Theory Previous Question Paper

1 | M- 72317 (S3)-213

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc.(Computer Science) (2013 & Onwards) (Sem.?4)
NUMBER THEORY
Subject Code : BCS-401
M.Code : 72317
Time : 3 Hrs. Max. Marks : 60
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 :
(a) Find G.C.D. of (49,210,350).
(b) Show that n is odd iff n ? l(mod2).
(c) Give an example to show that if ab ? 0(mod m), then a
/
? 0(mod m) and b
/
? 0 (mod m)
(d) Solve the linear congruence : 9x ? 21(mod 30).
(e) State Euclidean algorithm.
(f) State Euler?s theorem.
(g) State Wilson?s theorem.
h) Define Euler phi function.
(i) Calculate the value of ? ?(360).
(j) For n > 2, ? ?(n) is an even integer.

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1 | M- 72317 (S3)-213

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc.(Computer Science) (2013 & Onwards) (Sem.?4)
NUMBER THEORY
Subject Code : BCS-401
M.Code : 72317
Time : 3 Hrs. Max. Marks : 60
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 :
(a) Find G.C.D. of (49,210,350).
(b) Show that n is odd iff n ? l(mod2).
(c) Give an example to show that if ab ? 0(mod m), then a
/
? 0(mod m) and b
/
? 0 (mod m)
(d) Solve the linear congruence : 9x ? 21(mod 30).
(e) State Euclidean algorithm.
(f) State Euler?s theorem.
(g) State Wilson?s theorem.
h) Define Euler phi function.
(i) Calculate the value of ? ?(360).
(j) For n > 2, ? ?(n) is an even integer.

2 | M- 72317 (S3)-213

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.
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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