True or False: For all integers a, b, and c, if a divides b and b divides c, then a divides c. True O False

Q: If a, b. and c are integers such that a|b and c|b. then ac|b.

A: False

Q: An example of subtracting positive and negative integers that would result in a negative answer…

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Q: Suppose a and b are both integers that are greater than 1. What is Icm(a, a*b)? a None of the…

A: We have find the lcm of given numbers.

Q: MUI QUE If a and b are positive integers, which of the following can never be the gcd(56a, 63b)? (a)…

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Q: Assume that c and d are particular integers. Is 6c + 4d ² + 3 odd? 2

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Q: a

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

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Q: If x is divisible by 5 or y is divisible by 5, then xy is divisible by 5.

A: Let x is divisible by 5. Then x=5u for some natural number u.

Q: Assume a, b ER. a+b, a² + b², a³ + b³, and a + b for all integers. Prove that am + bm is an integer…

A: Let us assume that a,b∈ℝ where ℝ is the set of real numbers. It  follows that a,b∈ℤ where ℤ is the…

Q: Write the number 6 as a sum of three natural numbers in several different ways, and, in each sum,…

A: To be solved - Number 6 as a sum of three natural numbers in several different ways, and, in each…

Q: If p, q andr are primes and i is a positive integer, then the number of positive factors of p'q i…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Use two column proof and state reasons. Let x be the product of 5 distinct integers, where each of…

A: Given: Let x be the product of five unique integers, each of which is in the range of 1 to 63,…

Q: For all integers a, b and c, a|bc if and only if a|b and a|c True or False

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Q: Show that if p is a prime number, a and b are positive integers and p | ab, then p | a or p | b.

A: The objective is to prove that if p is a prime number, a and b are positive integers and p | ab,…

Q: a and b are positive integers, show that gcd(a,b) = gcd(a,a+b).  Discrete math questio

A: To prove that gcd(a, b) = gcd(a, a + b) for positive integers a and b, you can use the properties of…

Q: let a and b be integers. Show: if a * b is odd, then a is odd and b is odd

A: A number is even, if it is divisible by 2. A number is odd, if it is not divisible by 2. The odd…

Q: Write a (formal) proof of the following statement: "If 4 does not divide an integer n, then does not…

A: Here we have to prove if 4 doesn't divide an integer n, then 4 doesn't divide n2 -3n+5.

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

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Q: Prove by contraposition: if a, b and e are integers and be is not divisible by a, then b is not…

A: Given a,b and c are integers. Statement : P: bc is not divisible by a. Statement: Q: b is not…

Q: d = (a, b, c).

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Q: Let a and b two positive integers. Then we have that axb LCM(a,b) = GCD(a,b). O True O False

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Q: let a, b, and c be integers. if a divides c and b divides c, must a*b divides c?  Prove or come up…

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Q: If two integers have the same parity, then their sum is even. (Try cases.)

A: According to the given information it is required to prove that the sum of two integers of same…

Q: Consider these four statements: A: For all integers a, b, and c, if a | b and a | c then a|(2b –…

A: The objective is to find the correct statement.

Q: Prove this statement For all integers a, b, and c, if a ∤ bc, then a ∤ b

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Q: Use the following sets: A={Factors of 50} B={odd numbers} Which elements are found in A∩B?

A: A={Factors of 50} = { 1,2,5,10,25,50}  B={odd numbers} ={1,3,5,7,9,11,......}

Q: Prove the following statement: For any positive integers a, b, c and d: a+2cd or b-a2d if and only…

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Q: Use The Fundamental Theorem of Arithmetic to show If (a, b) = 1, a|c, and b|c, then ab|c.

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