4) Prove that the product of any three consecutive integers is divisible by 6.

Q: Prove, using the definition of odd, that for all integers r, that 6r+5 is odd.  b) true or false:…

A:

Q: 2. Prove that the product of any two odd integers is an odd integer.

A: Let x and y be two odd numbers. If a and b are odd, then a and b can be written as: x=2m+1 , y=2n+1…

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: Suppose an integer x is divisible by 21. What other positive integers must also divide x? [Hint:…

A:

Q: 3. Let a and b be positive integers. Express the positive greatest common divisor of a and b in…

A: The positive greatest common divisor (gcd) of two positive integers, a and b, can be expressed in…

Q: Prove that 3 divides 17k+1-2*5k+3+11k+3 whenever k is a nonnegative integer

A: The objective is to prove that 3 divides 17k+1-2*5k+3+11k+3 whenever k is a nonnegative integer

Q: Factor each of the following a) x-xー4a b)xペー64

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…

Q: (1) As usual, let (a, b) stand for the Greatest Common Divisor of a and b. Is it true that k(a, b) =…

A:

Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

A:

Q: Suppose that 75% of students attend lectures for a particular course and 20% of students fall the…

A: Conditional probability : Conditional probability is a measure  of the probability of an event…

Q: Prove that every integer n ≥ 2 can be written as a product of prime numbers.

A:

Q: Prove that 3 divides n³ +2n whenever n is a positive integer.

A: Introduction: Consider a starting point for which the assertion is correct. The proposition is true…

Q: n any positive integer n, there exist n consecutive composite integers

A: Given that given any positive integer n, show that there exist n consecutive composite integers.

Q: 2. Prove that the difference of an odd integer and an even integer is odd.

A: Prove that the difference of an odd integer and an even integer is odd

Q: Prove or disprove the following statement: the product of any 4 consecutive integers is divisible by…

A:

Q: Assume that in a given year the National Basketball Association has 28 teams, which are split into…

A: The Orlando magic plays four games against each of the other four teams in the division. So, in the…

Q: Show that for all integers a, b > 0, the number (a + b) – (a O b) is both nonnegative and even.

A:

Q: For each pair of integers r and s below, Find the greatest common divisor d. Then, find m, n, such…

A: To determine the greatest common divisor, d and then to find m and n such that d = mr + ns. (a) r=32…

Q: 3. Show that there exist 100 consecutive positive integers that are not perfect squares.

A: Here we have to show that there exists 100 consecutive positive integer that are not perfect square.…

Q: 2. Use Fundamental Theorem of Arithmetic to prove that the product of any two odd integers is an odd…

A:

Q: Find the negation of the following statement: "Every non-zero integer can be factored as a product…

A: We have to find the negative of the statement "Every non-zero integer can be factored as a product…