Fibonacci number, Mathematics

Assignment Help:

1. Suppose n ≡ 7 (mod 8). Show that n ≠ x2 + y2 + z2 for any x, y, z ε Z.

2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.

3. Prove that it is always possible to make postage of exactly n cents for all n ≥ 32 using only 5 and 9 cent stamps.

4. Prove that every fourth Fibonacci number is a multiple of 3.

In other words, show that 3 | f4n ∀n  ≥ 1.

5. Let bn be the sequence recursively defined by b0 = 1, b1 = 5 and, for n > 1,

bn = b[n/3]+2b[n/3]

(a) Compute b26 and b27.

(b) Guess a formula for bn when n = 3t for t ≥ 0 and then use mathematical induction to prove that your guess is correct. (Be sure to include a careful statement of what you are trying to prove).

 


Related Discussions:- Fibonacci number

Pi, pi to the ten-thousandths

pi to the ten-thousandths

Find the lesser of two consecutive positive even integers, Find the lesser ...

Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k

Scatter graphs, Scatter Graphs - A scatter graph is a graph that compr...

Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin

Apply depth-first-search to find out the spanning tree, Apply depth-first-s...

Apply depth-first-search to find out the spanning tree for the subsequent graph with vertex d as the starting vertex.        Ans: Let us begin with node'd'. Mark d as vi

Develop a linear program to investment advisory firm, An investment advisor...

An investment advisory firm manages funds for its numerous clients. The company uses an asset allocation model that recommends the portion of each client's portfolio to be invested

Binomial, how do you find the co=efficent when there are two brackets invol...

how do you find the co=efficent when there are two brackets involved?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd