Fibonacci number, Mathematics

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).

 

Posted Date: 2/26/2013 12:07:08 AM | Location : United States







Related Discussions:- Fibonacci number, Assignment Help, Ask Question on Fibonacci number, Get Answer, Expert's Help, Fibonacci number Discussions

Write discussion on Fibonacci number
Your posts are moderated
Related Questions
Caterer determines that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. I

In a digital filter, one of the parameters in its difference equation is given by the formula a) Show that the above formula has one horizontal and one vertical asymptote.

i have problems with math and my teacher said that i am still progressing in math

Systematic Sampling Systematic sampling is a part of simple random sampling in descending or ascending orders. In systematic sampling a sample is drawn according to some predet


Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du,     where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably


How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into