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

    1
    ReputationRep:
    Name:  kth.png
Views: 289
Size:  57.0 KB

    I've really thought about this but I can't seem to get to the required result. Any help on what to do is much appreciated.

    Thanks.
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by Peter8837)
    Name:  kth.png
Views: 289
Size:  57.0 KB

    I've really thought about this but I can't seem to get to the required result. Any help on what to do is much appreciated.
    If you're still working on this, the "x = y^k implies x^{(p-1)/d} = 1" is fairly easy by Fermat's Little Theorem, and part 2 follows quickly from part 1 by setting k=437, p=1013, and working out the HCF. Simple trick to simplify the HCF if you didn't spot it: hcf(1012, 437) = hcf(253, 437) by cancelling the spare factor of 4; = hcf(253, 184) because 437-253 = 184; = hcf(253, 23) by cancelling the spare factor of 8; and this is clearly 23. It's a bit faster than Euclid, to incorporate some very simple prime factor decomposition.
    Not quite sure about how to do "x^{(p-1)/d} = 1 implies x is a kth power"; I'll have another think.
    Offline

    0
    ReputationRep:
    For the other direction you need to write x=g^y were g generates the group. then p-1|(p-1)*y/d =>d|y.

    Also k=d*l where l coprime to p-1.

    By Euclidean Algorithm there is a so that a*l=1mod(p-1)

    I put the full solution in white.

    y*a*l=ymod(p-1)

    g^(y*a*l)=g^y=x

    also y*l=k*b

    Now y*a*l=a*b*k

    taking h=g^(a*b)

    h^k=x
 
 
 
  • 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
    What's your favourite Christmas sweets?
    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.