110ahw2 - Math 110A Homework #2 David Wihr Taylor Summer...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 110A Homework #2 David Wihr Taylor Summer 2006 1. Problem 1.3.1: Express each number as the product of primes: (a)5040, (b)- 2345, (c) 45670, (d) 2042040. Answer: To my knowledge there is no fast algorithm to factor primes that doesn’t use quantum computing (see Shore’s algorithm if you want to see how to factor on a quantum computer). If there were some conventional algorithm, then all computer encryption would be unsafe (same thing if anyone ever builds a quantum computer)! However, there is an algorithm that runs as a polynomial function of the size of the number you input that tells you if your number is prime. All this basically doesn’t help you do this problem, but it’s interesting stuff anyway. Mathematica tells me: (a) 5040 = 2 4 · 3 2 · 5 · 7 (b)- 2345 =- 1 · 5 · 7 · 67 (c) 45670 = 2 · 5 · 4567 (d) 2042040 = 2 2 · 3 · 5 · 11 · 13 · 17. 2. Problem 1.3.9: Claim. If p is prime and ( a, b ) = p then ( a 2 , b 2 ) = p 2 Proof. First we notice that if p divides both a and b then p 2 divides both a 2 and b 2 . Now let’s express a and b by their prime factorizations a =...
View Full Document

This note was uploaded on 11/03/2010 for the course MATH 262-338-20 taught by Professor Gieseker,d. during the Fall '10 term at UCLA.

Page1 / 2

110ahw2 - Math 110A Homework #2 David Wihr Taylor Summer...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online