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

Each child is unique in learning development, Each Child Is Unique :  Alth...

Each Child Is Unique :  Although every child goes through similar stages of development, the process may vary from one set of children to another, and also from one child to anoth

Shares and dividends, at what price 6.25% rs 100 share be quoted when the m...

at what price 6.25% rs 100 share be quoted when the money is worth 5%

Engg maths, How to get assignment to solve and earn money

How to get assignment to solve and earn money

Tower of hanoi problem, a) Write  a summary  on  Tower  of  Hanoi  Probl...

a) Write  a summary  on  Tower  of  Hanoi  Problem.  How  can  it  be solved using  recursion ?                  b) Amit goes to a grocery shop and purchases grocery for Rs. 23.

Unconditional and conditional probability, Independent and Dependent Events...

Independent and Dependent Events Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event

How to adding polynomials, How to Adding Polynomials? The numerical par...

How to Adding Polynomials? The numerical part of a monomial is called the coefficient. For example, the coefficient of 5x is 5. The coefficient of -7a 2 b 3 is -7. Like

Expressions, how do you solve expressions

how do you solve expressions

How to join as maths expert, Sir, I am a Maths teacher from kolkata,India....

Sir, I am a Maths teacher from kolkata,India.i want to join your website as Maths'' expert.Please guide me as to how to join your website and earn some money. I will be really grat

In terms of x what is the total number of miles they rode, Noel rode 3x mil...

Noel rode 3x miles on his bike and Jamie rode 5x miles on hers. In terms of x, what is the total number of miles they rode? The terms 3x and 5x are such as terms since they hav

Real numbers, how to present root numbers on a number line

how to present root numbers on a number line

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