Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    I am currently tackling questions of the form:
    if n exists in the integers, then 7 divides one of the following:

    n-4,n+2,n+5,n+6,n+11,n+14. True or False?

    I have the answer to this which tells me to divide each term by 7 and find the remainders, which are:

    n+3,n+2,n+5,n+6,n+4,n

    but I have no idea where these values have come from? Could anybody tell me where this comes from? Or provide me with a different method for solving this
    • Community Assistant
    Offline

    17
    ReputationRep:
    Community Assistant
    (Original post by gdickinson_)
    I am currently tackling questions of the form:
    if n exists in the integers, then 7 divides one of the following:

    n-4,n+2,n+5,n+6,n+11,n+14. True or False?

    I have the answer to this which tells me to divide each term by 7 and find the remainders, which are:

    n+3,n+2,n+5,n+6,n+4,n

    but I have no idea where these values have come from? Could anybody tell me where this comes from? Or provide me with a different method for solving this
    Hey I've moved this question to maths study help for you.

    Have you studied modular arithmetic?
    Offline

    22
    ReputationRep:
    (Original post by gdickinson_)
    I am currently tackling questions of the form:
    if n exists in the integers, then 7 divides one of the following:

    n-4,n+2,n+5,n+6,n+11,n+14. True or False?

    I have the answer to this which tells me to divide each term by 7 and find the remainders, which are:
    Look at modular arithmetic -4 \equiv 3 \pmod{7}, 11 \equiv 4 \pmod{7} since 11 = 7 + 4 so dividing by 7 leaves a remainder of 4. 14 \equiv 0 \pmod{7} since there is no remainder 14 = 2\times 7.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    Look at modular arithmetic -4 \equiv 3 \pmod{7}, 11 \equiv 4 \pmod{7} since 11 = 7 + 4 so dividing by 7 leaves a remainder of 4. 14 \equiv 0 \pmod{7} since there is no remainder 14 = 2\times 7.
    Hi, yes I am currently studying modular arithmetic. I under stand the examples you have given me but I can't make sense of my original question. Where does n come into it? What is n?
    Offline

    22
    ReputationRep:
    (Original post by gdickinson_)
    Hi, yes I am currently studying modular arithmetic. I under stand the examples you have given me but I can't make sense of my original question. Where does n come into it? What is n?
    n is just any integer.
    • Thread Starter
    Offline

    1
    ReputationRep:
    I see now! Is there any chance you can help me with 8 divides [2n], having the values {0,2,4,6}. I understand that 8 divides [n] gives {0,1,2,3,4,5,6,7}
    Offline

    22
    ReputationRep:
    (Original post by gdickinson_)
    I see now! Is there any chance you can help me with 8 divides [2n], having the values {0,2,4,6}. I understand that 8 divides [n] gives {0,1,2,3,4,5,6,7}
    Is this a different problem? What does the square brackets represent?
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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