Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    If 6x = 7(mod 11), how would we know/get to x = 3(mod 11), my minds gone blank on how to get to this.

    And also, if 5x = 4(mod13), how would we know/get to x = 6(mod 13)

    thanks
    Offline

    1
    ReputationRep:
    I'm fairly sure there's a principle of modular arithmetic that could solve that with a single line but I can't find my notebook atm.
    So we're taking the long way :p:

    6x = 7 (mod 11) => 6x = 18 (mod 11)
    By definition 6x-18=11k => 6(x-3)=11k (which means k is divisible by 6)
    => x-3=11k/6=11p (p=k/6) => x = 3 (mod 11)
    Offline

    1
    ReputationRep:
    Also, Z_{11} is a field since 11 is prime. Therefore, each number has an inverse. For example, 6^{-1}=2 because 6\cdot2\equiv1(\mod 11); I found it by trying different numbers. So, x = 7\cdot 6^{-1}\equiv7\cdot 2\equiv14\equiv 3 (\mod 11).
    Offline

    17
    ReputationRep:
    If the numbers are small, trial and error is really about as good as it gets.

    If the numbers are larger, e.g. 1234x = 5678 mod 7919, use the extended Euclidean algorithm.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 22, 2010
Poll
Do I go to The Streets tomorrow night?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.