Purchase Solution

Legendre Theorem and Prime Factors

Not what you're looking for?

Ask Custom Question

Let X and Y be independant random variables that are both equally likely to be either 1,2... (10)^N, where... a) Give a heuristic argument that Qk = 1/k^2Q1.
(See attachment for full questions)

Attachments
Purchase this Solution
Solution Summary

The Legendre Theorem and Prime Factors are investigated.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Please use words to describe the solution process. Send as word attachment

The probability that X (or Y) is divisible by k is 1/k. (For every k consecutive numbers, only one of them will be divisible by k.) If k|X and k|Y, then X/k and Y/k ...

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

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

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

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.

View More Free Quizzes
Related BrainMass Solutions

  • Theory of numbers

    Legendre symbol: Let p be a prime, and let a be an integer. The Legendre symbol is defined by Theorem 1: Let a and b be two integers and let p be prime.

  • Group theory

    ( p is odd prime and a an integer not divisible by p ) the LEGENDRE SYMBOL IS DEFINRD BY = 1 if a is a quadratic residue of P, = -1 if a is a quadratic nonresidue of P. a. Evaluate b. Evaluate Hint 4567 is a prime. c.

  • Jacobi Symbols and Proofs

    (d/p_s), where (d/p_k) is the legendre symbol mod p_k. 1. If b and c are odd, we can suppose b=p_1*...*p_s, c=q_1*...*q_r, where p_i (1<=i<=s) and q_j (1<=j<=r) are prime numbers. Then we have (a/bc)=(a/p_1)...(a/p_s)*(b/q_1)...

  • The Fundamental Theorem of Arithmetic and Prime Factors

    The fundamental theorem of arithmetic and prime factors are investigated and the details are discussed. The solution is detailed and well presented.

  • Square roots of prime numbers

    According to the Fundamental Theorem of Arithmetic, each of the integers p and q factors uniquely into primes. We get a contradiction. Then, the original statement was wrong and it is not rational.

  • Number Theory : Quadratic Residues

    I am trying to solve this problem myself (using that x^2-6 = 0 (mod p) => 6 is a quadratic residue mod p, and then try to find the form using the properties of the Legendre symbol (but if this is wrong, please discard it).

  • Chinese Remainder Theorem

    So, the lcm is given by multiplying all the prime factors by taking care that only maximum power is considered for common factors. So, lcm is given by 22x31x51x71=420. Chinese Remainder Theorem is applied.

  • Explain the Proof Step-by-step : If n is not a perfect square, then n^(1/2) is irrational.

    S(2): We may assume that r and s have no prime factors in common, since any common prime factors may be cancelled. S(3): From the first step, we have (s^2)*n = r^2. S(4): Suppose that s>1 and p is a prime factor of s.

  • Maximum Length of Repeating Fraction Pattern

    Now we add back in the factors of 2 and 5.

View More Related Solutions