Every odd prime number is greater than 2.

Q: Every integer n22 either is a prime or can be expressed of a product of primes. This statement is…

A: Every integer n≥2 is a prime or can be expressed as product of primes. This statement is Fundamental…

Q: Find the greatest natural number n such that n + 10 divides nº + 100.

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Q: Justify that every prime number except 2 and 3 has the form 6q + 1 or 6q + 5 for some integer q.

A: Let p be a prime number other than 2 and 3. If p is divided by 6, then by the quotient-remainder…

Q: Every natural number can be written as the products of prime numbers

A: Prime numbers are the numbers which have only two factors, 1 and the number itself.

Q: The number of factors of prime numberss are (None of the mentioned Depends on the prime number (2 (3

A: Prime number is only divisible by 1 and that number itself

Q: Every natural number greater than 1 can be written as the products of prime numbers.

A: Prove that  every natural number greater than 1 can be expressed as product of primes or the number…

Q: If p + 2 is a prime number, prove that p² + 3 is divisible by 4.

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Q: Find the number of ways a 5-digit positive integer can be made such that in each of them every digit…

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Q: Prove that 2" >n For all nuatural numbers

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Q: p + 2 is a prime number, prove that p2+3 is divisible by 4. (2.5

A: Prime and divisibility

Q: Find the smallest positive integer N that satisfies all of the following conditions: • N is a…

A: We have to find the smallest positive. N'that satisfies all of the following conditions: N is a…

Q: Every two different prime numbers are relatively prime. False True

A: In this question we need to check the given statement is true or false

Q: All prime numbers are odd.

A: We have state whether given statement is True or False. We know that  A prime number is a number…

Q: .If p 5 is an odd prime, prove that either p? – 1 or p² + 1 is divisible by 10.

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Q: The integers 77 and 105 are relatively prime. صواب İhi

A: By finding the factors of given numbers you can find the solution :

Q: Prore the only prime of the form n°-4 is 5.

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Q: Which of the following number below is an integer that is not a natural number?

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Q: If you randomly pick integers from 1 to 200, how many would you have to pick to ensure that at least…

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Q: (1) The integer 123 is a prime.

A: (1) Given, the integer 123 is a prime.

Q: Is the conjecture "all prime numbers are odd" true or false? O True O False

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Q: 4. Find all the prime numbers that can be expressed in the form n2 – 9 for some integer n.

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Q: The smallest prime numberis: 3

A: Prime number: A prime number is a whole number greater than 1 that can only be divided by itself and…

Q: If n is prime, then 2" – 1 is prime.

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Q: Suppose p and q are distinct prime numbers. Find the number of positive integers x ≤pq such that…

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Q: Determine how many ti (o bom is a prime.

A: In this question, the number of times is determined when 1 appears in the multiplication table for…

Q: Do you think it is worthwhile, or useful, to solve the puzzles proposed in Euclid's theorem of…

A: The objective is to solve the puzzles proposed in Euclid's theorem of primes There are infinitely…

Q: 2. For which odd primes p is 11 a

A: If p is a prime, then by Fermat's Little Theorem

Q: 8n? a prime number for every n = 1, 2, 3, . ...

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Q: Find all prime numbers pand of for which 2p²q + 45 pp ² = y² 2 де

A: Given:

Q: show that no integer of the form n^3+1 is a prime other than 2

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Q: All of the following statements about prime numbers are true except

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Q: If n is a perfect number, prove Σ d|n 1 2.

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Q: Prove that 2^(27) - 1 is not a prime number.

A: A prime number is a natural number greater than 1 that is not a product of two smaller natural…

Q: For every natural number n, one of n-1, n, or n+1 is a multiple of 3

A: The following two steps are used to prove a statement P(n) by the principle of mathematical…

Q: all > 4, 2" – 1 is not a prime number.

A: Statement is false

Q: . Prove that for each natural number n, /3n +2 is not a natural number.

A: Let n be any natural number.  n=3m+k2   =3m2+6m·k+k2   =9m2+6mk+k2   =33m2+2mk+k2 Here, m and k are…

Q: Determine the possibilities for the final digit of a sixth power of an integer.

A: The last digits of a number are 0,1,2,3,4,5,6,7,8 and 9. The number 0 raised to any number will be 0…

Q: The number of primes of the form n³ – 1 is 1) 1 2) 2 3) Infinite

A: To choose correct option

Q: -1

A: No it is not a prime numbers

Q: Show that the sum of twin primes p and p + 2 is divisible by 12, provided that p> 3.

A: Let p, p + 2 be twin primes. Then p *(p+1) + 1 = p^2 + 2p + 1 = (p+1)^2 ,  a perfect square.

Q: Show that if 2m +1 is an odd prime, then m 2" for some nonnegative integer n.

A: We solve this question by contradiction

Q: If n is an even integer, then 3n° is an even integer.

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Q: For each natural number n, if 3 does not divide (n² + 2), then n is not a prime number or n = 3.

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Q: Find all numbers p such that all six numbers p, p+2, p+6, p+8, p+12 and p+14 are primes.

A: For the given statement

Q: Let be a prime number (integer). Show that p2 + 5 cannot be a prime number.

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Q: Find all values of primes p for which (¹¹) = 1 Р

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Q: Every prime number is odd. True False

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Q: Every natural number n > 2 cam be writtenn = PiP2 Pr as the ... product of distinct prime numbers…

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Q: Find the least natural number a with the property that the sum a + 2ā + 3a + ...+ 9a is the number…

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Statements and Logic

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