The small positive integer n for which (1+i)?"=(1-i)?n is =..

Q: If k is an integer: exp[(i)(pi)(2k+1)] = ?

A: Given that: exp[(i)(pi)(2k+1)]

Q: An integer n is said to be abundant if o(n)>2n. Every multiple of abundant integer is abundant *…

A: We know,  abundant number is a number that is smaller than the sum of its proper divisors. An…

Q: For any positive integer n, n(n+1)(2n+ 1) EP = 12 +22 + .. + r?

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Q: Find an explicit formula for an if ao = 1 and an (n + 1)an-1+3" %3D for n > 1.

A: To Determine :-  An explicit formula for an if a0 = 1 and an =  n + 1an-1 + 3n for n ≥ 1.

Q: Give a formula for the nth positive even integer: Here is a theorem: 1+ 2+3 + ... + n п(n+1) n = Use…

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Q: Find a positive integer n for which the equality holds = 1 2

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

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Q: 1. Compute the value of (), for n > 3.

A: Formula: nr=n!r!n-r!

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: Given n < 10" for a fixed positive integer n°2, prove that (n + 1)* < 10*1.

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Q: Find the smallest integer value c and it's n, to show that 2n2 + 6n – 3 Oln –10) is an

A: Given:

Q: For each nonnegative integer i, what is the least residue modulo 9 or 10i?

A:

Q: Prove that 2" < n! for any integern 2 4

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If p times tne pth term of an A.P. is equal to q times the qth term of the same AP., then how that…

A: Given that If p times the pth term of an A. P. is equal to q times the qth term of same A. P.  To…

Q: of the first 150 positive integers?

A:

Q: Prove that the sum of the first n cubes is equal to the square of the sum of the first n positive…

A: According to the given information, it is required to prove the following.

Q: Show for all integers n> 1 that 7 I (3ªn+l – 5²n-1 ).

A: a) Prove 734n+1-52n-1 for all integers n≥1 by mathematical induction as follows. Basis step: For…

Q: Every even integer greater than 2 is sum of two primes? Give your views on this?

A: We know that 2 is even prime. And all other primes are odd.

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: Question 2. Show that for any integer n, 5|(n5 − n).

A: The given statement is that "for any integer n, 5|n5-n". By Principle of Mathematical Induction,…

Q: Disprove the claim: 3 m E N such that m > 3 and m? – 1 is a prime number.

A: The claim is given : ∃ m∈N such that m≥3 and m2-1 is a prime number Now, m2-1=(m-1)(m+1)--(1) Case…

Q: 1. Prove that Si-2' = (n – 1) - 2"*+1 + 2 for any positive integer n.

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Q: Before arriving at his famous conjecture, Goldbach had conjectured that every odd positive integer…

A: Goldbach conjecture says that every integer greater than 5 is the sum of three primes.

Q: What is the smallest integer n for which 25n&gt;512?

A: The provided expression is as follow:

Q: 1. Use PMI to show that for any n E N, 4 divides 5" - 1.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: For how many positive integers 'n', n3-8n2 + 20n - 13 is a prime?

A: Introduction :

Q: For all integers n> 0, 32n – 1 is divisible by 8.

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Q: integer of the form okts is also but not' conversely

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Q: Is the following statement true or false? n+1 For every odd integer n, To answer this question, let…

A: Given statement true or fasle For every odd integer n {n /2} = n+1 /2

Q: 27 en+1 – 1 < 0.05 ? 2 (n + 1) · (n + 1)!

A: Given: The expression is, 272en+1-1n+1n+1!. Calculation: Obtain the value n such that…

Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

A:

Q: If n is a positive integer, is there always a prime between n and 2n?

A: given that n is a positive integer. we have to show that there is always a prime number between n…

Q: For every integer n23 I+ 2+ 2?+ +4^= 4(4n-16) %3D 3. Proof (by induction)

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Q: Show that for n ≥ 3, ô(n) is even.

A: We have from the definition of Euler ϕ function: ϕ(1)=1 and ϕ(2)=1 Now Let n ≥ 3

Q: 2) If n is an odd integer, then H= (n-1) 2

A: To prove that n2=n-12 such that n is an odd integer.

Q: 3. Determine the nth-term formula for the number of square tiles in the nth figure. а. a2 a4 as b.…

A:

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.

Q: Prove that 2^? +3^? is a multiple of 5 for all odd ?∈N.

A: We will solve this problem using principle of mathematical induction.

Q: Prove the following: for all integers n > 5, n2 < 2"

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Q: Show that for any integer n ≥ 2, C(2n,n) > C(2n,n-1)

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Q: Show that the n-th tetrahedral number O_n is given by S_n= n(2n^2+1)/3

A: A tetrahedral number corresponds to a 3-Dfigure in the shape ofa tetrahedron made of spherical…

Q: tn be a positive integer and M = [2 01 %3D en M" 2n equal to the above None of the mentioned

A:

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

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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: give direct proof by contradiction that is 5n-1 is odd, then n is even

A:

Q: (-i)ñ is e(1+2n)i where n is an integer. equal to the above O None of these +4n where n is an…

A: To solve this question we shall use the following identity      Identity:                   eiθ=cos…

Q: Prove or disprove the following: n+1 For any odd integer n, H= ()) 2

A: Let  n=2k+1         -  (1) Where k is an integer. Then n is any odd integer. Now, LHS= n24        -…

Q: There is an integer n such that 7n2 – 5n + 11 is a prime number. -

A: Let fn=7n2-5n+11for n=1f1=7×1-5×1+11      =13 , which is prime number for n=2f2=722-5×2+11…

Q: 5. Find all integers 100 ≤ n ≤ 999 such that the last three digits of n² is same as n.

A: To find: All integers  100≤n≤999 such that the last three digits of n2 is same as n.