Number Theory MATH-6258 exam answers

Find the Least Common Multiple: 2 and 7

35
21
14 Correct
10

Find the Least Common Multiple: 3 and 11

44
22
33 Correct
55

Find the Least Common Multiple: 3 and 7

28
18
35
21 Correct

Find the Least Common Multiple: 4 and 15

70
30
45
60 Correct

Find the Least Common Multiple: 4, 6 and 8

28
32
16
24 Correct

Find the Least Common Multiple: 4, 8 and 10

65
30
40 Correct
60

Find the Least Common Multiple: 5 and 7

25
70
45
35 Correct

Find the Least Common Multiple: 6 and 14

56
42 Correct
49
28

Find TWO common multiples of the given numbers: 2 and 5

15 and 30
5 and 15
10 and 20 Correct
20 and 25

Find TWO common multiples of the given numbers: 3 and 4

12 and 16
8 and 12
12 and 24 Correct
15 and 21

Find TWO common multiples of the given numbers: 4 and 5

20 and 30
10 and 20
15 and 40
20 and 40 Correct

Find TWO common multiples of the given numbers: 5 and 11

5 and 55
5 and 33
55 and 110 Correct
55 and 125

Find TWO common multiples of the given numbers: 8 and 9

32 and 72
72 and 144 Correct
56 and 64
54 and 144

From the given numbers, which number has more number of factors?

25
45
15
30 Correct

From the given numbers below, _______ is the coprime of 143.

None of the choices
13
19 Correct
11

From the given numbers below, _______ is the coprime of 286?

19 Correct
2
13
11

Given: 162 = 256 = ___ (mod 27), what must be the value of the unknown?

13 Correct
14
12
15

Given: 202 = 400 = 22 (mod ___), what must be the value of the unknown?

17
23
15
27 Correct

Given: 22 = 4 = 32 (mod ___), what must be the value of the unknown?

26
28 Correct
22
24

How many divisors does 12 have?

8
4
6 Correct
10

How many factors does 421 have?

2 Correct
3
4
5

How many primitive roots below 100 does 421 have if the coprimes are between 5 and 11, using 3 as base?

3
0
2
1 Correct

IF a number is divisible by _________, multiply 3 to the last digit then add the remaining number Repeat the steps if necessary This rule applies in

Divisibility of 29 Correct

If a number is divisible by 11, the last 3 digits must be divisible by 11.

True
False Correct

If a number is divisible by 23, multiply the last digit of the given number to 7 and add the remaining number. Repeat the steps if necessary.

True Correct
False

If a number is divisible by 31, multiply the last number to 3 and subtract from the remaining number. Repeat the steps if necessary.

True Correct
False

If a number is divisible by 37, multiply 11 to the last digit minus the remaining number. Repeat the steps if necessary.

True Correct
False

If a number is divisible by 43, multiply 13 to the last digit of the number and add to the remaining number. Repeat steps if necessary.

True Correct
False

If a number is divisible by 47, multiply 14 to the last digit of the number and add from the remaining number. Repeat the steps if necessary.

True
False Correct

If k is less than 0 where k is not an integer, then f(0) is undefined and it has no y-intercepts.

True Correct
False

If one of the factor of 420 is 14, the other one is____.

30 Correct
28
20
23

If the integers 5, 3, -4, 7, -10, 8, and -5 are arranged in order from least to greatest which integer would come first in the list.

8
3
-10 Correct
-4

If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.

True Correct
False

If the values of k are odd integers, thus the function has a certain symmetry.

True
False Correct

If we substitute 7 for s, from the formula 2s + 1, then the answer is ____.

128
135
129 Correct
50

If we substitute 7 for s, from the formula 2s + 1, then the answer is ____. Is the answer a Fermat number?

Maybe
No answer
No Correct
Yes

If you obtain the factors of 444, the largest prime number is

23
11
37 Correct
3

If you substitute 5 to the Fermat form, the answer is ________?

32
31
11
33 Correct

If you substitute a negative integer to the exponent of a power function, then the answer is _____________.

singularity Correct
symmetry
none of the choices
anti-symmetry

In a power function the base is a variable and raised to a fixed exponent.

True Correct
False

In finding the answer in 59 mod 5, the usual last step of congruence modulo is

The remainder is the answer Correct
Divide 59 and 5
Multiply the whole number to 5
Subtract the product to the first whole number

In mod 33, using 2, 3, and 5 as coprimes and base 5, the primitive roots are 8, ____, and ____.

21 and 23
23 and 25
25 and 26
23 and 26 Correct

Johnny borrowed money from his brother 10 months ago. He returned Php 1000.00 per month to his brother starting the month he borrowed the money. Currently, he owes his brother Php 5,000.00. How much money did he borrow from his brother?

Php 20,000
Php 15,000 Correct
Php 10,000
Php 12,000

Listed below are three numbers that are composite. Which is not?

681
878
577 Correct
785

Power function is presented in the form f(x) = abc.

True
False Correct

Simplify the expression 32 x 52 x 7 = ?

1575 Correct
1225
1455
1305

The _____________ is the modulo of a certain number.

remainder Correct
sum
difference
product

The expressions below are all , EXCEPT:

53 = 125 = 10 (mod 15) Correct

The expressions below are all correct, EXCEPT:

53 = 125 = 10 (mod 15) Correct
39 = 19 683 = 48 (mod 55)
24 = 16 = 7(mod 9)
25 = 32 = 4 (mod 7)

The expressions below have a solution of 10.

78 mod 17 Correct
45 mod 23
72 mod 15
33 mod 21

The expressions below have a solution of 12, EXCEPT:

78 mod 17 Correct
47 mod 35
33 mod 21
72 mod 15

The factors of 12 from the given factor tree are 3 and ____.

2
4 Correct
3
6

The factors of 14 in the factor tree are 7 and ____.

3
4
2 Correct
5

The factors of 270 with the most times repeated is

3 Correct
7
5
2

The factors of 30 in the factor tree are

5 and 6 Correct
3 and 7
6 and 2
4 and 5

The factors of 300 are the prime numbers 2, 3 and 5. Which of the following numbers appears twice?

2 and 3
2 and 5 Correct
2, 3 and 5
3 and 5

The factors of 355 are ____ numbers.

4
2 Correct
5
3

The factors of the number is 25 x 32 x 37. What is the number?

7,104
5,787
5,328
10,656 Correct

The Fermat form is in the form __________.

2s - 1
2s - 1
2s + 1
2s + 1 Correct

The following are sets of integers, EXCEPT

{ 05, 1/3,} Correct
{-2, -5, -7,=E2=80=A6}
{1, 2, 3,=E2=80=A6}
{-3, -5, -7,=E2=80=A6}

The following are the divisors of 60, EXCEPT:

12
18 Correct
15
3

The following are the factors of 72, EXCEPT:

12
8
6
23 Correct

The following are the multiples of 12 between 120 and 450, EXCEPT?

270
432 Correct
362
182

The following are the multiples of 2, 3, and 7, EXCEPT:

72
126
42
21 Correct

The following are the multiples of 3 and 5, EXCEPT:

{30, 60, 90,=E2=80=A6}
{3, 6, 9,=E2=80=A6 5, 10,=E2=80=A6}
{15, 30, 45,=E2=80=A6}
{3, 7, 9,=E2=80=A6 5, 10,=E2=80=A6} Correct

The following are the numbers you can multiply to produce the fundamental theorem of arithmetic, EXCEPT:

53, 59, 61, 67, 71, 73
3, 5, 7, 11, 13, 17
31, 37, 41, 43, 47, 49, 51 Correct
3, 37, 61, 71, 73

The following are the other quadratic residues of modulo 28 , EXCEPT

21
25
27 Correct
20

The following are the other quadratic residues of modulo 28, EXCEPT:

4
8
1
13 Correct

The following are the primitive roots of mod 50 base 2, EXCEPT:

12
5 Correct
14
28

The following are the quadratic non residue of modulo 27, EXCEPT

16 Correct
14
15
17

The following are the quadratic non residue of modulo 28, EXCEPT

25 Correct
23
22
24

The following are the quadratic residue of modulo 27 , EXCEPT

8 Correct
7
3
4

The following are the quadratic residue of modulo 28 , EXCEPT

10 Correct
8
9
4

The following expressions are , EXCEPT:

None of the choices Correct

The following expressions are correct, EXCEPT:

None of the choices

Number Theory

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