Module 3 Quiz Module 3 Quiz

Module 3 Quiz - Results

Attempt 1 of 1

Written Nov 9, 2023 5:30 PM - Nov 9, 2023 5:55 PM

Attempt Score 12 / 20 - 60 % Overall Grade (Highest Attempt) 12 / 20 - 60 %

True or False

Question 1

Every non-empty subset of the integers that is bounded above has a greatest member.

Question 2

A positive integer has one prime factorization, not counting rearrangements.

Question 3

If n > 2 is composite then there exists a prime integer q that divides n and Your quiz has been submitted successfully.

True False

True False

Question 4

Question 5

All Diophantine equations have an infinite number of solutions.

Question 6

If a ≡ b mod m then m|(b-a).

Question 7

If 3 divides the sum of the digits of a positive integer then 9 divides the integer.

2 ≤ q ≤ n 2

True False

 The Euclidean Algorithm can be used to find  a ⁻¹ mod m

 when  gcd (a, m) ≠ 1.

True False

True False

True False

Question 8

A rational number with an infinite binary expansion can have a finite decimal expansion.

Question 9

Question 10

The congruence class representative modulo m of a^-1 is the unique integer between 0 and m such that a⋅a^-1 ≡ 1 mod m.

Question 11

When operating modulo 17, 23⋅9=3.

Fill in the blanks True False

True False

 If 2 ^p−1 ≡ 1 mod p then p is prime.

True False

True False

True False

Question 12

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Question 13

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Question 14

___39___ (28) Modular Arithmetic Question 15

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Question 16

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How many distinct prime numbers are factors of 28994625 ? (Enter a digit(s) not a word)

How many digits are there in the hexadecimal expansion of the base ten number 2557761073 ?

How many 1 bits are there in the binary expansion of

(Enter a digit(s) not a word)

2 ³⁹ − 2 ¹¹ ?

Recall: The congruence class representative modulo m of a^-1 is the unique integer between 0 and m such that a⋅a^-1 ≡ 1 mod m.

Solve 3x ≡ 4 mod 7. Enter the congruence class representative of the answer in the blank.

Recall: The congruence class representative modulo m of a^-1 is the unique integer between 0 and m such that a⋅a^-1 ≡ 1 mod m.

Enter the congruence class representative of 31^-1 mod 13 in the blank.

Question 17

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Question 19

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Question 20

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Done

Recall: The congruence class representative modulo m of a^-1 is the unique integer between 0 and m such that a⋅a^-1 ≡ 1 mod m.

Enter the congruence class representative of 13^-1 mod 31 in the blank.

Let X= 9³⁶⁰¹. Then X is congruent to what number mod 13? Your answer must be an integer between 0 and 13.

Let X= 9³⁶⁰¹. Then X is congruent to what number mod 31? Your answer must be an integer between 0 and 31.

What is the remainder when 9³⁶⁰¹ is divided by 403?