1. ᶲ(231)=

a) 230

b) 60

c) 80

d) 120

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2. n is prime if and only if n divides (2^{n} – 2).

a) True

b) False

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3. Find x for the CRT when x= 2 mod 3; x= 3 mod 5; x = 2 mod 7

a) 33

b) 22

c) 23

d) 31

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4. Consider a function: f(n) = number of elements in the set {a: 0 <= a < n and gcd(a,n) = 1}. What is this function?

a) Primitive

b) Totient

c) Primality

d) All of the mentioned

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5. The inverse of 49 mod 37 is –

a) 31

b) 23

c) 22

d) 34

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^{-1}mod 37 = 34.

6. Six teachers begin courses on Monday Tuesday Wednesday Thursday Friday and Saturday, respectively, and announce their intentions of lecturing at intervals of 2,3,4,1,6 and 5 days respectively. Sunday lectures are forbidden. When first will all the teachers feel compelled to omit a lecture? Use CRT.

a) 354

b) 371

c) 432

d) 213

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7. How many primitive roots are there for 25?

a) 4

b) 5

c) 7

d) 8

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Given 2 as a primitive root of 29, construct a table of discrete algorithms and solve for x in the following –

8. 17 x^{2} = 10 ( mod 29 )

a) x = 3, 22 (mod 29)

b) x = 7, 28 (mod 29)

c) x = 2, 27 (mod 29)

d) x = 4, 28 (mod 29)

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9. x^{} – 4x – 16 = 0 (mod 29)

a) x = 6, 24 (mod 29)

b) x = 9, 24 (mod 29)

c) x = 9, 22 (mod 29)

d) x = 6, 22 (mod 29)

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10. x^{7} = 17 (mod 29)

a) x = 8, 9, 12, 13, 15, 24, 28 (mod 29)

b) x = 8, 10, 12, 15, 18, 26, 27 (mod 29)

c) x = 8, 10, 12, 15, 17, 24, 27 (mod 29)

d) x = 8, 9, 13, 15, 17, 24, 28 (mod 29)

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11. The inverse of 37 mod 49 is –

a) 23

b) 12

c) 4

d) 6

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^{-1}mod 49 = 4.

12. How many primitive roots are there for 19?

a) 4

b) 5

c) 3

d) 6