prove that, it ņ is an 3n+2is oald then integer and nis add

Q: find a Positive integern for which the equality holds %3D

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Q: Show with the help of Fermat’s little theorem that if n is a positive integer, then 42 divides n7 −…

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Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: Prove that 1+1=2

A: To prove: 1 + 1 = 2

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A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

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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.

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Q: Using Fermat’s little theorem to show that 42 | n7 −n, where n is a positive integer.

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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: 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: Prove that 3 divides n³ +2n whenever n is a positive integer.

A: Introduction: Consider a starting point for which the assertion is correct. The proposition is true…

Q: b) Prove that () - 2) = n², where n is a positive integer.

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Q: Show that yn for all n=1, 2₁- ✓

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Q: Prove that 4 divides 6 7" - 2.3" for all integers n 20.

A: We need to prove that 4 divides 6.7n-2.3n for all integers n≥0.

Q: S²₁ Sinmxsinhxbx = 2 x if m=n So min

A: To prove:- ∫-ππsinmxsinnxdx=0if m≠nπif m=n

Q: Prove that n2 + 4 is not divisible by 3 for all integers n.

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

A: Let d be gcd of a and b. Now, b is odd so d cannot be even or is odd.  Now, since d is odd and…

Q: Show that for positive integer n: (-1)" - 22n . n! VT. (2n)!

A: Given: n is a positive integer. To Show:Γ12-n=-1n·22n·n!2n!π.

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 that tim 51

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let x and y be positive integers. When is x + y3 a prime number? When is x+y a composite number?…

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.