Is it true that for any odd n the number 2" +1 is divisible by 3? Prove your answer.

Q: 15) n(n*+5) is divisible by for each integer

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Q: How might you tell if a number is even or odd in bases two, three, four, five, six, seven, eight,…

A: Given data:- The given numbers are 2, 3, 4, 5, 6, 7, 8, 9, 10 Explain the generalize to bases of n.

Q: Prove that N × N × N is countable. Does your argument generalize to the Cartesian product of k…

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Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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Q: the fourth power of an integer is x, and x is between 100 and 600. What is x?

A: It is given that the fourth power of an integer is x.That is, x = n^4, where n is a positive…

Q: If N =30 -1. Is N is divisible by 125?

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Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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Q: If n is an integer, then 2n + 1 is odd

A: Given , n is an integer We have to show that 2n+ 1 is odd

Q: Prove, by induction, that n + 3n2 + 2n is divisible by 6, for n 2 0.

A: In this problem I have use mathematical induction method two times please read step by step.

Q: show that n(n^2-1)(n+2) is divisible by 4 for all integers n

A: To show that n(n^2-1)(n+2) is divisible by 4 for all integers n

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

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: How can I prove by induction that 2^n + 1 is divisible by three for all odd integers

A: To apply mathematical induction to show that 2^n+1 is divisible by 3 if n is odd

Q: Prove: For any integer n, if n2 is divisible by 4, then n is even

A: I'm proving this using by contradiction.

Q: 4. n(n+ 1)(n + 2) is divisible by 6

A: We have to check

Q: If n is an integer and 3n + 2 is even then n is even. (You may use any kind of proof)

A: Given: To prove that if n is an integer and 3n+2 is even then n is even.

Q: If n is a natural number, the number 34n+4 – 43n+3 is divisible by: -

A: Given : To find : A positive number which can divide above expression

Q: Show that if n is a positive integer then =n(n + 1)2"-2

A: We know the binomial theorem formula isx+yn=∑k=0nCkn xn-kyk, where Ckn is the binomial co-efficient…

Q: What is the smallest integer n for which 25n>512?

A: The provided expression is as follow:

Q: (b) An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

A:

Q: Prove that the product of an even number and an odd number is even.

A: Here, objective is to prove that the product of an even number & an odd number is even

Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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Q: Prove that 6-1 is divisible by 5 for any n 21.

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Q: 2. Prove that n(n + 1)(n + 2) is always divisible by 6

A: We have to show that the number nn+1n+2 is always divisible by 6 for all n∈ℕ. Let Pn=nn+1n+2 where…

Q: that if 3 divides the sum of the digits of n, then 3|n

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Q: Show that (n + 1)! > 2"+3, for n > 5.

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Q: Prove that 9? −1 is divisible by 8,for all n ≥ 1

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Q: Show that if n is an odd integer then []

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Q: А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

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Q: Show by contradiction that for any integer n: if n>0, then n+10 n+5

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Q: positive

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Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers n.

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Q: (c) Prove that n? + 1 is not divisible by 3 for every integer п.

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Q: Prove that 3n^2 + 1is divisible by 4 whenever n is an odd number.

A: Using induction method we have to prove that 3n^2 +1is divisible by 4 where n is odd number.

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

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

A: To choose correct option

Q: (a) Prove that 82n – 12" is divisible by 13 for all nɛ N.

A: As per guidelines we are supposed to solve maximum one questions at a time.kindly post another…

Q: If  n×k divisible by 4, then n is divisible by 4 or k is divisible by 4. Which of the following is…

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Q: Prove by Induction that for every natural number п, 3h-1 is a multiple of 2?

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

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Q: 2. 6n – 1 is divisible by 5 for n any positive integer

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Q: For any natural number n, n²+1 is always odd. True False

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Q: For all ? ≥ 1, ?3 + 2? is divisible by 3. Prove using Principle of Mathematical Induction.

A: Let P(n) be the given statement i.e.,  P(n): n3 + 2n is divisible by 3 (for all n greater than or…

Q: For the previous problem how did you calculate for 1,5,17,and 37 for proving that n^2 + 1 is not…

A: Solution

Q: Prove by induction that the sum of the first n odd numbers is n². In other words, prove E1(2i – 1) =…

A: To prove by induction that the sum of the first natural numbers is n^2.

Q: 2 ) + ("**) = n²- .2 2

A:

Q: Prove that n(n + 1)(n + 2) is always divisible by 6

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Q: divisible

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