Download OU B.Sc 2018 May-June 2nd Year 2nd Semester 7113 Mathematics Question Paper

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Code No. 7113/ E

FACULTY OF SCIENCE

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B.Sc. IV-Semester (CBCS) Examination, May / June 2018

Subject: Mathematics

(SEC-2) Paper - IV

Number Theory

Time: 1½ Hour Max.Marks: 40

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Note: Answer all questions. Each question carries equal marks.

PART - A (2x5=10 Marks)

[Short Answer Type]

1. a) Show that 41 divides 2²⁰-1 using congruences.
2. b) Evaluate f (8400), t (8400).

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OR

1. a) If n is an even integer show that f (2n) = 2f(n).

OR

1. b) For any integer a, show that a³³⁷ = a (mod 1729) using Euler's theorem.

Note: The questions carries equal marks.

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1. a) Define µ(n). Show that Σ μ ( d ) = { 1 if, n=1 0 if, n>1 }

OR

1. b) State and prove Euler’s theorem.