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

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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.

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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: (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 a positive integer n we have that 33n+3 – 26n – 27 is divisible by 169. - -

A: The given expression is: 33n+3-26n-27 This is to be proved that the expression is divisible by 169.

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A: answer

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Q: Find all integers n > 1 such that 1n − 1)" is +2+...+(n divisible by n.

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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

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Q: Prove by cases that n2−1 is divisible by 3 when n is an integer not divisible by 3.

A: The detailed solution is given below Thank you

Q: Show that for all integers m and n, if the remainder is 2 when m is divided by 4 and the remainder…

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

A: Consider the provided expression,

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Q: Show that any integer of the form 6k + 5 is also of the form 3j + 2, but not conversely.

A: 2. We can write 6k+5 = 6k+3+2=3(2k+1)+2 lets write 2k+1=j hence 6k+5=3j+2

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

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

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Q: In an inductive proof that for every positive integer n, n п(п + 1)(2n + 1) Σ 6. j=1 what must be…

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Q: For any non negative integer n , prove that an – bn is divisible by a-b,where a and b are any…

A: Use the binomial factorisation