Prove that for a positive integer n we have that Bn+3 - 26n – 27 is divisible by 169.

Q: 2. Prove that 11" – 7" is divisible by 4 for any positive integer п.

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Q: Let n be an integer. Prove that if 2n3 +4 is divisible by 4, then n is even.

A: n is an integer. To show: 2n3 + 4 is divisible by 4 then n is even.

Q: Prove that for any positive integer n, 6(7") – 2(3") is divisible by 4.

A: We use binomial expansion formula for an-bn to solve the above problem.

Q: Use mathematical induction to prove that (3n + 7n − 2) is divisible by 4 for all integers n ≥ 1.

A:

Q: Prove that for a positive integer n we have that  33n+3 - 26n - 27 is divisible by 169.

A: To show  33n+3 - 26n - 27 is divisible by 169.

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

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Q: 5. Write the formal proof that 2"+2 + 32n+1 is divisible by 7 for all positive integers.

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Q: Prove that for any integer n, n6k - 1 is divisible by 7 if gcd(n, 7) = 1 and k is a positive…

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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 1 +,+ i++ = 2 – for all positive integers n. |

A: We want to prove 1 + 12 + 14 + ... + 12n = 2 - 12n

Q: For every positive integer n, prove that 7n – 3n is divisible by 4.

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Q: (2) Prove by mathematical induction that for all integers n > 0, the number 42n+1 + (21 · 33"+1) is…

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Q: Prove that 5n-1 is divisible by 4 to any positive integer n

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Q: Prove that for a positive integer n we have that 33n+3 – 26n – 27 is divisible by 169.

A: Topic - principle of mathematical induction

Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

Q: 4. Prove that given any integer for n, n3 + 2n will be divisible by 3. 5. Write the formal proof…

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

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Q: Prove that if for some integers a, b, c we have that a° + 6° + c° is divisible by 9, thên at least…

A: Here we have to prove that if for some integers a,b,c we have that a3+b3+c3 is divisible by 9,then…

Q: If n is a positive integer prove that 3^(2n) - 26n -1 is divisible by 676

A: if n is a postive integer prove that 3^(2n) - 26n -1 is divisible  by 676

Q: Prove that for any n E N, nº + 2n is divisible by 3.

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Q: Prove that n3 + 2n is divisible by 3 for all n E N.

A: We prove that n3+2n is divisible by 3 for all natural numbers n.

Q: Use the Principie to prove the Ving 3n+1 – 1 is divisible by 2 for all n > 0

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Q: Prove that n2-n is divisible by 2 for every positive integer n

A: We have to prove that,  n2-n is divisible by 2 for every positive integer n. We will use…

Q: Use induction to prove that for every integer 15"+2 + 162n+1 is divisible by 241. n > 0,

A: To use mathematical induction to prove the given statement

Q: Prove that for all positive integers n, 4n-1 is divisible by 3.

A:

Q: Prove that if n is an integer and 5n + 6 is even, then n is even.

A:

Q: Show that 3·4n+ 51 is divisible by 3 and 9 for all positive integersn

A: Consider the provided expression,

Q: Use mathematical induction to prove that 2n+2 + 32n+1 is divisible by 7 for all integers n 2 0.

A: Steps to perform Mathematical Induction: 1) Consider an initial value (say n = 1) for which the…

Q: Prove that there is no integer n for such that 5n+3 is divisible by 5.

A:

Q: Prove that 13n13 + 11n" is always divisible by 24.

A: Consider the given expression.

Q: Prove by induction that (2n+1)3 is an odd number for all positive integers n.

A: First principle mathematically induction : Suppose is a mathematical statement .Here n is a natural…

Q: Prove that2.7n + 3.5n – 5 is divisible by 24, for all n ∈ N.

A:

Q: Prove that 13n13 +11n is always divisible by 24.

A: We prove this by induction on n.

Q: Prove that n3+(n+1)3+(n+2)3 is divisible by 9 for all non-negative integers  n.

A:

Q: If 2n + 1 is prime for some n ≥ 1, prove that n is a power of 2.

A: We have given 2n +1 is prime for some n ≥ 1 We have to prove that n is a power of 2.

Q: Prove that n² +n is divisible by 2, where n E N.

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Q: .. (a) Prove by mathematical induction that 9**2 – 8n – 17 is divisible by 64 for all positive…

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Q: Prove that n2+n  is  divisible by 2, where nN.

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Q: Prove that for all n E N, 7" +2 is divisible by 3.

A: We will use mathematical induction to prove the result in question 4.

Q: Use the PMI to prove that 6" – 1 is divisible by 5 for every integer n > 0.

A: To prove that 6^n-1 is divisible by 5 for every integer greater that or equals to 0.

Q: Prove 8 divides 34h+1+52h+1 whenever h is a positive integer

A: We need to prove that 8 divides 34h+1+52h+1 whenever h is a positive integer by Mathematical…

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: Prove that 8" – 14n + 27 is divisible by 7, for all positive integers n.

A: The objective is to prove 8^n-14n+27 is divisible by 7.

Q: Prove, using mathematical induction, that 8n−3n is divisible by 5 for all integers n≥0.

A:

Q: 5. Prove that for any integer n, at least one of the integers n, n+2, n +4 is divisible by 3.

A: According to guidelines we can solved only ist question thank you   we have to Prove that for any…

Q: A. Prove that n3 + 2n is divisible by 3 for all integers n.

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Q: 1. Prove: 11" – 6 is divisible by 5 for all positive integers, n.

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Q: If n is an odd integer, show that n4 + 4n2 + 11 is of the form 16k.

A: Solution: The objective is to show that given equation is of the form 16k

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

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