1 (1 point) Question 1 options: Use information from the textbook to answer the question. Fill in the blank. The natural number a is by the natural number b if there exists a natural number k such that a = bk. View hint for Question 1 Save Question 2 (1 point) Question 2 options: Use information from the textbook to answer the question. Fill in the blank. A natural number greater than 1 that is not is called composite. View hint for Question 2 Save Question 3 (5 points) Use information from the textbook and the "Factoring" video to answer the question. An aid in determining whether a natural number is divisible by another natural number is called a divisibility test. For each number, identify the proper test to determine if it is a divisor of a given number. Question 3 options: The last digit is even. The last digit is 0. The last digit is 0 or 5. The sum of the digits is divisible by 9. The sum of the digits is divisible by 3. 1 divisible by two . 2 divisible by three . 3 divisible by five . 4 divisible by nine . 5 divisible by ten . View hint for Question 3 Save Question 4 (1 point) Use information from the textbook and the "Factoring" video to answer the question. Determine whether the statement is true or false. Every natural number can be expressed in one and only one way as a product of primes (if the order of the factors is disregarded). Question 4 options: True False View hint for Question 4 Save Question 5 (1 point) Use information from the textbook and the "Prime Number Formulas" video to answer the question. Determine whether the statement is true or false. If n is a composite number, then the Mersenne number 2n - 1 is also a composite number. Question 5 options: True False Save Question 6 (1 point) Use information from the textbook and the "Prime Number Formula" video to answer the question. Determine whether the statement is true or false. Euler's formula n2 - n + 41 generates primes for n up to 46 and fails at n = 47. Question 6 options: True False Save Question 7 (1 point) Use information from the textbook and videos to answer the question. Determine whether the statement is true or false. Every natural number of the form 4k + 5 is prime. Question 7 options: True False View hint for Question 7 Save Question 8 (1 point) Use information from the textbook to answer the question. Determine whether the statement is true or false. The proper divisors of a natural number include all divisors of the number except 1. Question 8 options: True False Save Question 9 (1 point) Use information from the video "31 and Mersenne Primes" to answer the question. Determine whether the statement is true or false. If M = 2n - 1 is a Mersenne prime, then (2n - 1)(2n)/2 is perfect. Question 9 options: True False View hint for Question 9 Save Question 10 (1 point) Use information from the textbook to answer the question. Determine whether the statement is true or false. All prime numbers are also deficient numbers. Question 10 options: True False View hint for Question 10 Save Question 11 (1 point) Use information from the textbook to answer the question. Determine whether the statement is true or false. All composite numbers are also abundant numbers. Question 11 options: True False View hint for Question 11 Save Question 12 (1 point) Use information from the textbook to answer the question. Determine whether the statement is true or false. A natural number which is not deficient must be abundant. Question 12 options: True False Save Question 13 (1 point) Use information from the textbook and the videos to answer the question. Determine whether the statement is true or false. There is no largest prime number. Question 13 options: True False Save Question 14 (1 point) Use information from the textbook to answer the question. Determine whether the statement is true or false. Twin primes are prime numbers whose difference is a multiple of 4. Question 14 options: True False Save Question 15 (1 point) Question 15 options: Use information from the textbook and the videos to answer the question. Fill in the blank. A natural number is said to be if it is equal to the sum of its proper divisors. View hint for Question 15 Save Question 16 (1 point) Use information from the textbook to answer the question. Fill in the blank. One of the most most famous unsoved problems in mathematics is called _______________ and states, "Every even number greater than 2 can be written as the sum of two prime numbers." Question 16 options: Goldbach's Conjecture None of these Primorial Primes Conjecture Twin Primes Conjecture View hint for Question 16 Save Question 17 (1 point) Use information from the textbook and the video "Sieve of Eratosthenes" to answer the question. Determine whether the statement is true or false. When determining whether a natural number is prime or composite, it is never necessary to check if the number is divisible by a prime greater than the square root of the number. Question 17 options: True False Save Question 18 (1 point) Question 18 options: Use information from the "Infinite Primes" video to answer the question. Fill in the blank. The mathematician who proved there are infinitely many primes around 300 B.C. was named . Save Question 19 (1 point) Use information from the textbook and the video "1 and Prime Numbers" to answer the question. Determine whether the statement is true or false. The number 1 is currently considered to be the only natural number that is neither prime nor composite. Question 19 options: True False Save Question 20 (1 point) Use information from the textbook and the "Prime Number Formulas" video to answer the question. Select all answer choices that are correct. Which of the following are names of mathematicians credited with formulas used to generate prime numbers? Question 20 options: Escott Euclid Mersenne Euler Save Question 21 (1 point) Use information from the video "8128 and Perfect Numbers" to answer the question. Determine whether the statement is true or false. It is unknown whether or not there are infinitely many perfect numbers. Question 21 options: True False Save