Let f(sub-n) denote the nth Fibonacci number. Show that f(sub-n) is even if and only if n is divisible by 3.

Q: Show that An, n > 5 is simple.

A: Sol:- To show that An, the alternating group of even permutations of degree n, is simple for n ≥ 5,…

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: The Fibonacci numbers are defined by fi = fz = 1 and fn+1 = fn+ fn-1 for n > 2. (a) Prove that…

A: (Solving the first question as per our guidelines) Solution: The Fibonacci numbers are defined by…

Q: TRUE OR FALSE  x and y are POSITIVE integers.

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Q: Find integers ? and ? such that 3220? + 6006? = gcd(3220,6006).

A: Remark: The greatest common divisor (gcd) of two integers is the greatest integer that divides both…

Q: Evaluate the sum. 20 3) Σ 3 k = 4

A: NOTE: Refresh your page if you can't see any equations. . here k is not starting from 1, it starts…

Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

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Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Show that 2 + V5 is imational number

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Q: let a = 3^4 7^3 11^2 13^5 and b = 2^6 5^2 7^2 11^3 13^4 Determine the values of (a,b) and [a,b] and…

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Q: Vx x² >0

A: Integer, whole-valued positive or negative number or 0. The integers are generated from the set of…

Q: 7. Mario has P18,000 in his bank account. He withdraw consecutively P7,300 and P2,300. After two…

A: There are certain question in your sheet. I am solving question 7. if you want all the questions to…

Q: Find an odd integer o written as an expression using the variable k with the property that when f is…

A: Here we have given a mapping  which proves that both the sets have same cardinality.

Q: Prove the property of the Fibonacci numbers, F(n) = 5(n 4) + 3F(n-5), for n ≥6

A: We have to prove the property of the given Fibonacci numbers F(n) = 5F(n-4) + 3F(n-5) ,  for n≥6

Q: Question the iff {an} one {bn3 are juro sequences Such that an = (x)2h + (yjzh and bn= (x)2th -(y)zh…

A: Introduction:       A grouping of numbers in a specific order is known as a sequence. On the other…

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: Please provide justified answer asap:::: Show that n is odd if and only if n^2+4n+1 is even.

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Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…

Q: Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest…

A: Given that, A numver is, 2n - 1 Where n = 2, 3, 4, 5, 6, 7, ............ We have to find the…

Q: 2 ) + ("**) = n²- .2 2

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Q: The operation * is defined over the set of real numbers "R" by a * b = a + b + 1/2ab. What is 6 * (2…

A: Given that the relation defined on real number R as a*b=a+b+12abTo find 6*(2*5)?