Prove that if n is a positive integer, then 133 divides 11"+1 + 122n-1

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

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A: Given: n be any integer. To prove: n3+4 is not divisible by 8.

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

A: I have proved the result using mathematical induction

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A:

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A:

Q: Prove that the statement is true for every positive integer n.

A: To prove: 1+4+7+...+3n-2=n3n-12

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A:

Q: Let n ∈ ℕ. Show that either √n is either an integer or it is irrational.

A: We have, n∈N Assume that  n=a2b2,where a,b are positive integers with no common factors other than…

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: Prove that if n is an integer, then 3n? + n + 14 is even

A: Case I - Let n be an odd integer , then n= 2k+1 where k is an integer. Then 3n2+n+14   =…

Q: Prove that if n is a positive integer, then 133 divides 11"+1 + 122n-1

A:

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.

Q: 24. Show that if p is a prime and k is an integer such that 1sksp-1. then p divides ().

A: 24. we have to show  that for a prime p with r≤k≤p-1      p divides  pk  Notation: pk=p!p-k! k!

Q: Number theory.

A:

Q: Prove that the statement is true for every positive integer n.

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Q: Show that for any integer n > 5, the integers n, n+2, and n +4 cannot all be primes.

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Q: . Prove that 3| (52n – 1) for every integer n 20.

A: Solution:  To show :   3|(52n-1)     , for every integer n≥0

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A:

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A:

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Q: Let n be an integer. Prove that if 7 divides (n – 2) or 7 divides (n – 5), then 7 divides (n² + 3).

A:

Q: Prove that if n is an integer and 3n + 2 is even, then n is even using a) a proof by contraposition

A: Given , n is an integer .To prove → if 3n+2 is even , then n is even using a proof by composition…

Q: Prove by Mathematical Induction that for any natural number n the number 52n+1 – 22n+1 is divisible…

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Q: Prove that N ≈ O*, where N is the set of natural numbers, and O* is the set of positive odd…

A: To prove:

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Q: show that no integer of the form n^3+1 is a prime other than 2

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Q: Prove that a positive integer n is p

A: Topic :- Number system

Q: Prove or disprove that for every positive integer n, if n is even then n^{2}+1 is prime.

A: False

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

A:

Q: Prove: If a is a positive even integer and b is an odd integer, then (a,b)=(a/2, b).

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Q: 11. Prove that for each integer a, if a? - 1 is even, then 4 divides a?

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Q: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even.

A: Given: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even

Q: Prove that if p is a prime integer, then 3√p is irrational.

A: To Prove that: If p is a prime integer, then 3√p is irrational.

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

A:

Q: Prove that 30 divides n° – n for every nonnegative integer n. -

A: The given question can be solved as shown in step2.

Q: Prove that if n is an integer, then 2n2 + n + 1 is not divisible by

A: The given problem is to prove the following statement using the possibile cases. We need to find the…