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

Patrice has worked a certain how many hours has she worked, Patrice has wor...

Patrice has worked a certain amount of hours so far this week. Tomorrow she will work four more hours to finish out the week along with a total of 10 hours. How many hours has she

Difference between experiment and outcome, Difference Between Experiment an...

Difference Between Experiment and Outcome Experiment is an operation that produces outcomes which can be observed. Outcome/Event is the result of an experiment.

6thgrade, do you have 3 digit and 4 digit number problem

do you have 3 digit and 4 digit number problem

Probability, a die was rooled 500 times and number of times 4 came up was n...

a die was rooled 500 times and number of times 4 came up was noted if the imperical probability calculated from this information 7_10

Sketch the graph f ( x ) = - x5 + (5/2 )x4 + (40/3) x3 + 5, Sketch the grap...

Sketch the graph of the below function. f ( x ) = - x 5 + (5/2 )x 4 + (40/3) x 3 + 5 Solution : Whenever we sketch a graph it's good to have a few points on the graph to

Statistics, if the sum of mean and variance of a binomial distribution is ...

if the sum of mean and variance of a binomial distribution is 4.8 for five trials, the distribution

Example of making connections of a child with maths, After a lot of effort,...

After a lot of effort, 8-year-old Hari worked out 2 x 88 = 176. When asked to say what 2 x 89 was, after a lot of hard work, he produced the answer 178. How would you help him to r

Find the maximum and minimum brightness values, Variable stars are ones who...

Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.

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