Use cases to prove that for all integer n, n2+3n+5 is odd.

Q: Show that for every integer n, n³ + 2 is not divisible by 4.

A: Here, we use rules of divisibility.

Q: Prove that 5 does not divide 5n+3 for any integer n.

A:

Q: Find a positive integer n such that 2n is a square and 3n is a cube.

A: Sol:- Let 2n be equal to x², where x is a positive integer. Then, n can be written as n = x²/2.…

Q: Use induction to show that n4 + 15 is a multiple of 16 for every positive odd integer n.

A:

Q: nd the smallest positive integer N such that n+2 3n-4 -}| < < 0.01 for all n ≥ N.

A: We want to find N such that n+23n-1 - 13 &lt; 0.01    for all   n ≥ N

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: 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: Use contradiction to prove:  if 3n + 2 is an odd integer, then n is odd.

A: consider 3n+2 as odd integer  and let  n is even  therefore, n=2k for some integer k therefore,…

Q: Prove that 6 divides n3-n for all non-negative integers n.

A: See the detailed solution below.

Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: Show that if k is a positive integer, then (15k+4)/(10k+3) is in lowest terms.

A: We use the concept of Ring theory that a fraction is in lowest form if the gcd of numerator and…

Q: Show that if n is an integer and 5n + 6 is odd, then n is odd. (Use contradiction.)

A:

Q: Prove that 4 does not divide n2 +2 for any integer n.

A:

Q: Use proof by cases to prove that for any integer n, n² + 3n + 7 is even.

A:

Q: Use proof by contradiction to show that for all integers m, 7m+4 is not divisible by 7.

A: Recall the following fact about divisibility.

Q: Prove that 2n>n2 if n is an integer greater than 4.

A: According to the given information, it is required to prove the given statement.

Q: Prove that if n is an odd integer then 7n+5 is even.

A: Given Statement: Prove that if n is an odd integer then 7n+5 is even

Q: Find all positive integers n for which n1º +1 is divisible by 10.

A:

Q: Use the method of proof by cases to prove that for any integer n the product n(n + 1) is even

A: Given,  for any integer n the product n(n + 1) is even  We have to prove it using the method of…

Q: n2 - 2 is

A:

Q: Prove that 2n + 3 ≤ 2n if n is an integer greater than 3.

A: Sol :- To prove:- 2n+3&lt;=2^n if n is an integer greater than 3 We prove this by induction For n=4…

Q: Prove this statement For any integer n, n2 + 5 is not divisible by 5.

A: The given statement, For any integer n, n2+5 is not divisible by 5. We have to prove this statement.

Q: Use proof by contradiction to show that the sum of two odd integers(k and l) is eve

A: An even number is a number that is divisible by two. All even numbers finish with one of the digits…

Q: prove n2 + 5 greater than or equal to 4n for all integers n

A:

Q: Use proof by contradiction to prove that for every integer n, if n 2 − 6n + 5 is even, then n is…

A: