Purchase Solution

Binary Representations and Prime Factors

Not what you're looking for?

Ask Custom Question

1- For n belongs to N (set of natural numbers) let B(n) denote the number of digits used in the binary representation of n. For example
B(1) = 1;
B(2) = 2;
B(3) = 2;
B(4) = 3:

Find a closed formula for B(n) for an arbitrary n belongs to N.

2: Prove that if gcd(a, b) = d then a/d and b/d are relatively prime.

3- Find the smallest prime factor of (p1)(p2)...(pk) +1, where p1, p2, ... pk are the kth smallest primes for all positive integers k not exceeding 50.

Purchase this Solution

Solution Summary

Binary Representations and Prime Factors are investigated.

Solution Preview

1. B(n) is the smallest integer which is greater than or equal to log(base 2) n.
In another word, we can find some integer k, such that 2^(k-1)<n<=2^k, then B(n)=k.

2. Proof: if a/d and b/d are not relatively prime, then they have a common factor r>1. Then
we have a/d=rx, ...

Purchase this Solution


Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.