math 311w homework7 - animated and by the time some...

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

View Full Document Right Arrow Icon
Homework 7. Due Monday, March 29 Problem 1. Let p be a prime number. Prove a) Z p does not have divisors of zero. b) Prove that equation x 2 1 mod p has only two solutions and find them. c) Prove that ( p - 1)! + 1 is divisible by p . Problem 2. Find all solutions or explain why there is no solutions: a) 6 x 4( mod 15) b) 6 x 3( mod 15) c) 102 x 24( mod 240) Problem 3. Find the last two digits of 7 7 7 . Problem 4. Find all integer x such that x 2 mod 5 x 3 mod 4 x 7 mod 11 Problem 5. A hoard of gold pieces ”comes into the possession of” a band of 15 pirates. When they come to divide up the coins , they find that three 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
are left over, Their discussion of what to do with these extra coins becomes
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: animated and by the time some semblance returns there remains only 7 pi-rates capable of making an eective claim on the hoard, When, however, the hoard is divided between these seven it is found that two pieces are left over. There ensues an unfortunate repetition of the earlier disagreement, but this does at least have the consequence that the four pirates who remain are able to di?vide up the hoard evenly between them, What is the minimum number of gold pieces which could have been in the board? 2...
View Full Document

This note was uploaded on 10/13/2010 for the course MATH 311W taught by Professor Mullen during the Spring '08 term at Pennsylvania State University, University Park.

Page1 / 2

math 311w homework7 - animated and by the time some...

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