Prove that if n is an even integer greater than 2, then 2 - 1 is a composite.

Q: Prove that if a is an odd integer, then 5a² – 3a + 5 is odd.

A:

Q: Prove that the product of any k consecutive positive integers is an integer multiple of k!.

A:

Q: (12) Let p be a prime integer, p≥ 5. Prove that p² - 1 is divisible by 24.

A:

Q: Prove that if n is an odd integer, show that n⁴ + 4n² + 11 is expressible in the form 16k for some…

A:

Q: Show that for positive integer n,

A:

Q: 1. Prove that nº + n is even for every integer n.

A:

Q: Prove that every positive integer n>1 has a prime factorization.

A: Prime factorization is a way of expressing a number as a product of its prime factors.

Q: Prove or disprove: For every positive integer n, 22n – 1 is divisible by 3. -

A: I have proved the result using mathematical induction

Q: Prove that if n is an even integer greater than 2, then 2 - 1 is a composite.

A:

Q: Prove that for any integer n, we have n - 2 is not divisible by 4.

A:

Q: 4. Show that for all positive integers n, n! + 1 has a prime divisor greater than n.

A: Let n be an integer such that n>1. All prime divisors of n!+1 must be bigger than n. This is…

Q: Prove that for any odd positive integer, n, the sum of nconsecutive positive integers is divisible…

A: To prove for any odd positive integer, n, the sum of nconsecutive positive integers is divisible by…

Q: Prove that n²– 3n + 1 is odd for every integer n.

A: To prove that n^2-3n+1 is odd for every integer n.

Q: Prove that 3 devides 17k+1-2*5k+3+11k+3whenever k is a non-negative integer.

A:

Q: Jse a direct proof to show that if n² is an odd integer, then n* is also an odd integer.

A: Given, n² is an odd integer. So, n² = 2k+1, where k is an integer. Now, n⁴ = (n²)² = (2k+1)² = 4k² +…

Q: Prove that 3n+2 and 5n+3 are relatively prime for every integer n.

A: We have to prove that and  are relatively prime for every integer .We know thatThe greatest common…

Q: Show that for every positive

A:

Q: Prove that the integers n, n+2, n+4 are all primes if and only if n=3

A: Statement: Prove that the integers n, n+2, n+4 are all primes if and only if n=3 Proof by…

Q: b) Prove that () - 2) = n², where n is a positive integer.

A:

Q: Prove that the fourth power of any integer has the form 4k or 4k + 1 for some integer k.

A: We have to prove the following -  The fourth power of any integer has the form 4k or 4k+1 for some…

Q: 6. Prove that 2n +5 and 3n+7 are relatively prime for every integer n.

A: What is Relatively Prime Numbers: Relatively prime or coprime numbers are two such numbers which…

Q: Prove that a positive integer n is prime number.if no prime p less than or equal to n divides n.

A: Let us assume that the contradiction of the statement , let  n ≥ 0 be a composite number .  Thus , n…

Q: prove that n²_1 is divisible by when ever n is odd an Positive integer.

A:

Q: prove that it ņ is an 3n +2 is odd then integer and is add

A: This is related to Number System

Q: Suppose n is an integer. Prove that if n is even, then n²+3n+5 is odd.

A:

Q: Prove: Any positive integer can be represented as an aggregate of different powers of 3, the terms…

A: