Prove or disprove: There are inline number of primes

Q: Find all primes that are the difference of the fourth powers of two integers.

A: Let the two integers are x and y and n is prime so we have  n=(x4-y4)       (suppose x>y)…

Q: Suppose that n is a positive integer with the properties: • for any integers a, b, c, • n is not…

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Q: Suppose that p is a prime integer greater than 1755. What is the largest possible value of (p,…

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Q: Covert to an equalivent statement to a universal statement:"6 is the smallest postive integer that…

A: According to the given information, It is required to write the statement into universal statement.…

Q: Prove: If x is a positive prime integer, then x+7 is a composite integer. (i.e., not prime)

A: See solution below

Q: Show that there is a prime number p such that p+4 and p+6 are also prime numbers.

A: Prime number is a number p having only two divisors p and 1 only.

Q: 2. What are the prime factors for the below numbers and arrange them in a canonical form. a. 17 b.…

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Q: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

Q: : a number is even  if

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Q: Determine the number of ways a computer can randomly generate one or more such integers from 1…

A: There are 5 prime numbers between 1 to 12 . Which are 2 ,3 , 5, 7 , 11.

Q: 10 ation: an integer or rational number in the

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Q: Determine all the primes p such that p^2 77 has exactly 5 positive divisors.

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Q: Assuming that p, q, r are distinct primes, how many positive divisors does m have in the following…

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Q: Let p, q be distinct primes. Show that pq is an irrational number.

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Q: Suppose that p is a prime integer greater than 1238. What is the largest possible value of (p,…

A: Given that p is a prime greater than 1238.

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Q: Give a counterexample to the statement. The product of 2 primes is always odd.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.