(a) Suppose that there are k distinct positive integers that divide an odd positive integer n. distinct positive integers divide 2n? How many divide 4n? (b) Suppose that there are k distinct positive integers that divide a positive integer n that is not divisible by 3. How many distinct positive integers divide 3n? How many divide 9n? How many

Q: How many integers from 1 to 700 (inclusive) are divisible by the factors of 70 greater than 1?

A:

Q: Suppose you work at a restaurant as a waiter. One night, only you and a coworker are staffed. At the…

A:

Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

A:

Q: Use the roster method to write the set of integers between 0 and 12

A:

Q: A number n is divisible by 12 if it satisfies ∃k ∈Z(n = 12k) Give a direct proof that, if n is…

A:

Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that are…

Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that…

Q: divisible by 3 for

A:

Q: How many integers in {1, 2,..., 100} are not divisible by 7 or 5? (Give the exact number)

A: Find the number of integers in 1,2,...,100 which are not divisible by 7 or 5.

Q: (8) How many integers in the set [1,000] = {1, 2, ..., 1,000} are (a) divisible by 5? divisible by…

A:

Q: (3) Prove that if a cube of a number is divisible by 17, then the number is divisible by 17.

A: We have to prove that if cube of a any number is divisible by 17 then the number itself is divisible…

Q: How many integers in {1,2, 3, ..., 99, 100} are not divisible by 7? (Give the exact number)

A: The given set of numbers is, 1,2,3,.....,99,100 The total no.of numbers from 1 to 100 is, 100 The…

Q: If k is a positive integer, what is the remainder when (k+ 2)(k3 - k) is divided by 6? Stilo…

A:

Q: Suppose you work at a restaurant as a waiter. One night, only you and a coworker are staffed. At the…

A:

Q: (2) You roll a die 8 times and tabulate the results, counting the total number of 1s, 2s, 3s, 4s,…

A: Given the event of rolling a die 8 times

Q: (6) Find the sum of the integers for 7 to 508 Tmelusive,

A: first term (a0) = 7last term( an) = 508,     d = 1 ( natural no.)first we have to find total no of…

Q: 2. Factor 10+1 into a product of primes for k = 1,2,3,4,5.

A:

Q: (a) How many different collections of 50 coins can be chosen if there are at least 50 of each kind…

A:

Q: MK18. Show that in any set of 9 integers chosen from the set {2,3, 4, ... , 21, 22}, there are at…

A: