Question The cube of any integer may has the form: 9k + 8 9k + 7 O This option This option 9k + 6 All of the choices O This option This option

Q: Proposition 9. Let n be a non-negative integer. Then 1+2+4+ 8+ ...+ 2" = 2"+1 – 1.

A: To prove the above statement we can use the method of induction. In which first we show that the…

Q: 7. The number 2022 has three distinct prime factors, a, b, and c. The number 2022! can be factored…

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Q: Let A⊆B. Which of the following statements is/are true? a. A∩B ⊆ A       b. AUB⊆B         c. A\B is…

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Q: One integer is 5less The shan another integer. Product Of the integers is acH. Find the intebers.…

A: let x and y be the two integers

Q: Fermat's little theorem states that if p is a prime number, then for any integer a, the number a P…

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Q: How many statements are TRUE? i. 5 is a factor of 15. ii. 15 is a multiple of 5. iii. 15 is a factor…

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Q: 20.What is the largest possible integer that could be the length of the third side of the triangle?…

A: We can find the answer using the properties of triangle and the given option

Q: A Cryptarithm The following puzzle is a famous cryptarithm. Each letter in the cryptarithm…

A: To Find -

Q: you’re thinking of a number 1-50 and i have to guess what it is. i asked these questions in this…

A: Given: A numbers between 1-50. To find: Find a number greater than 25, divisible by 2, 3 and 5 and…

Q: The following statement (if z is a natural number then z is an integer) is correct. Choose one of…

A: An integer is a whole number ( not a fraction number) that can be positive, negative, or zero. The…

Q: -J: State whether each of the following statements is true or false. Then give an explanation, proof…

A: As per our guidelines we can answer only one question. please repost other seperately.  Use binomial…

Q: 1. p: There is an integer x such that x? = 4. 2. q: x + 7 >9 3. r: I am a millionaire! %3D

A: Note: According to Bartleby guidelines; for more than 3 questions asked, only the first three are to…

Q: You are told that the following two statements are true: If Alex is a student, then Alex reads a…

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Q: Questions: a. Are there numbers whose squares are smaller than the numbers themselves? b. A prime…

A: a.  there is number all number greater than themselves  but the number between 0 to 1 whose square…

Q: S SC equals SC none of these Question 3 (1 point) Saved Listen Given: Set S consists of all positive…

A: 2)    S 3)    divisible by 18

Q: Tell whether the following integer an even or odd integer using the form 2k and 2k+1 8 7

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Q: Question X: The expression 2x2 + 11 is prime for all integers x with 1) 0 < x < 10 2) 0<x< 11 3)…

A: Given expression is 2x2+11. We have to find the all integers for which expression 2x2+11 is prime.…

Q: The greatest common divisor of two number 1, b(integer) are b+1 (1) None of the mentioned

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Q: Bob is a stamp collector. His collection consists of three books. Two-tenths of his stamps are in…

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Q: 7.) A positive integer is 5 more than the second positive integer, and the product of these two…

A: 7. Let second positive integer be x. Given first positive integer is 5 more than second integer. So,…

Q: give a direct proof of "if m is odd integer, then m^2+1 is even integer"

A: Recall that if n is an integer then n² is Always an integer.

Q: Find the length of the segment AB. -10 -9 -7 -6 -5 -4 -3 -2 9. 10 The length is (Type an integer or…

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Q: Which of the following is False There is only one prime of the form n2 - 4. O This option 5 is the…

A: 1)  There is only one prime of the form n2-4We have,n2-4=n-2n+2Since for n = 1, 2, n2-4 is negative…

Q: Question * If a and b are two integers such that a is even and b is odd, then gcd(a,b) # gcd(a/2, b)…

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Q: How many integers from 0 through 60 can be picked such that at least one that is odd? at least one…

A: Since we have  integers from 0 to 60. we know that from 1 to 60 half numbers are even and half of…

Q: b+c c+a a+b If a, b, c are positive integers prove that + + b C a > 6.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Question * If a is an integer such that (a, 11) = 1, then 11 divides: a5 – 1 or a5 + 1 a5 – 1 This…

A: I am solving this in step 2

Q: 1 9'5 o V3, V14, V27 Which of the following sets of numbers are irrational? 7, 11, 23

A: To find the set of irrational number313, 29, 153, 14, 277, 11, 23

Q: Find U A and N1A, where: a. A, = {-i,-i + 1, ...,–1,0, 1, ..,i – 1, i} for every positive integer i.…

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Q: Question Which of the following is True (Chose all correct answers) There are many primes of the…

A: Concept: Number theory: The study of the set of positive whole numbers 1, 2, 3, 4, 5, 6, 7,...,…

Q: Question * Which of the following is True (Chose all correct answers) There are many primes 5 is the…

A: no, It is not  true that there are many primes in the form of n3-1  The only lower number prime is…

Q: Consider the statement: for all integers a and b, if a is even and b is a multiple of 3, then ab is…

A: (a) The given statement is as follows. For all integers a and b, if a is even and b is a multiple of…

Q: Question * The cube of any integer may has the form: 9k + 8 9k + 7 This option This option 9k + 6…

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Q: square of any odd integer is od.

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Q: Which one represents the following statement? If k is not an odd positive integer then square of k…

A: Option (b)

Q: Suppose a is some natural number and that GCF (a, 24) = 1. Determine whether the following…

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Q: Question Let a and b be two positive integers such that gcd(a, a? – b?) = 1. Then, ged(a + b, a² –…

A: Given that a and b are two positive integers and gcd(a,a^2-b^2) = 1. We now check which of the given…

Q: Question * Let a and b be two positive integers such that gcd(a, a² – b?) = 1. Then, - gcd(a + b, a²…

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Q: c. How many subsets of A contain only even numbers? d. How many subsets of A contain an even number…

A: As per the question we are given the following set : A = {1, 2, 3, 4, 5, 6, 7, 8, 9} And we have to…

Q: Suni et z (e) If n is a real number and n>2, then n'>4. If ns 2, then" (d) Either a positive integer…

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Q: 22 Jlgull The number of factors of prime numbers are None of the mentioned O 2,0 3 0 Depends on the…

A: 2

Q: 2. Calculate: a. (3,3) + (5,6) b. (4,3) + (5,6) c. (2,5) + (4,2) Say that the two pairs (a, b) and…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 21. What is the smallest possible integer that could be the length of the third side of the…

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Q: Question A positive integer is 7 less than another. If 6 times the reciprocal of the smaller integer…

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Q: Question Which of the following is True (Chose all correct answers) There are many primes 5 is the…

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Q: Identify whether or not the given sentence is a proposition. 1. There is a number that satisfies the…

A: Proposition and sentence.

Q: Identify the axiom of real numbers illustrated. Give a complete answer, such as Commutative Axiom…

A: Identify the axiom of real numbers illustrated. Give a complete answer, such as Commutative Axiom…

Q: 5. Which of the following option is true? A. If the Sun is a planet, then elephants will fly. B. 3+2…

A: To find which of the given statement is true.

Q: Question * Let a and b be two positive integers such that gcd(a, a² – b?) = 1. Then, gcd(a + b, a² –…

A:

Q: 2.Which of the following option is true? *       a) If the Sun is a planet, elephants will fly…

A: The given statements are: