Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Official TSR Mathematical Society

Announcements Posted on
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    TSR was the cause for quite literally doing nothing in terms of school work and I thought this would have affected my exams (considering I had done no homework in any of my subjects) and I need three a for Oxford. Considering how my exams have recently gone though I found that you can quite literally learn whole modules in one or three days - subject specific - ergo TSR time.
    Lol fair enough.
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    This is the same person :rolleyes: ...
    lmao!
    • 10 followers
    Offline

    ReputationRep:
    Prettier rep though.
    • 1 follower
    Offline

    ReputationRep:
    (Original post by The Muon)
    lmao!
    Anymore wall challenges?
    • 0 followers
    Offline

    ReputationRep:
    how about something simple, criticise the logical paradox in the statement:
    "This statement is false"

    lol dean you made a new accout because your rep was low :rofl:
    • 1 follower
    Offline

    ReputationRep:
    Quickie.

    Sir Gustaff is happy when smoking ciggareetes and drinking wine. So happy his happyness is proprtional to the square of the number of bottels of wine he has in one day multiplied by the packets of ciggarettes he has in one day. A bottle of wine costs 3 pounds, ciggarettes cost 2 pound. He has an allowance of 100 pounds. What amount of alcohol and ciggarettes should Gustaff acquire to achive greatest happyness?
    • 1 follower
    Offline

    ReputationRep:
    question
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    question
    answer :p:
    • 1 follower
    Offline

    ReputationRep:
    (Original post by The Muon)
    answer :p:
    Prove that  \sqrt{2} + \sqrt{3} is algebraic
    Spoiler:
    Show
    not a good problem
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    Prove that  \sqrt{2} + \sqrt{3} is algebraic
    Spoiler:
    Show
    not a good problem
    Spoiler:
    Show
    it is a solution of  x^4 - 10x^2 + 1 = 0 . i think this suffices...
    • 1 follower
    Offline

    ReputationRep:
    (Original post by GHOSH-5)
    Spoiler:
    Show
    it is a solution of  x^4 - 10x^2 + 1 = 0 . i think this suffices...
    A quaint paper 2 question;

    4) Prove there are infinitely many integers [distinct] that are positive such that  x^2 + y^3 is divisible by x^3 + y^2
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    A quaint paper 2 question;

    4) Prove there are infinitely many integers [distinct] that are positive such that  x^2 + y^3[/late] is divisible by [latex]x^3 + y^2
    is this from a BMO-2?
    • 1 follower
    Offline

    ReputationRep:
    (Original post by GHOSH-5)
    is this from a BMO-2?
    correct
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    correct
    out of curiosity, do you actually have a solution to the problem?
    • 1 follower
    Offline

    ReputationRep:
    (Original post by GHOSH-5)
    out of curiosity, do you actually have a solution to the problem?
    I do
    • 1 follower
    Offline

    ReputationRep:
    (Original post by JohnnySPal)
    I know I'm being hick here, but why doesn't the solution set {(x,x) : x \in \mathbb{N}}
    Oh. Yeah I made that mistake at the first time I read it.

    (x,y) are such that  x \ne y - distinct.
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    I do
    a hint by any chance?
    • 1 follower
    Offline

    ReputationRep:
    (Original post by GHOSH-5)
    a hint by any chance?
    It would considereably give the game away as the hint is the solution.

    Spoiler:
    Show
    Don't open three spoilers below before thinking hard
    Spoiler:
    Show
    Why wlog can you assume something about (x,y) ?
    Spoiler:
    Show
    assume y > x
    Spoiler:
    Show
    y = kx
    • 1 follower
    Offline

    ReputationRep:
    Solution;

    Spoiler:
    Show
    Let y = kx  \Rightarrow \frac{x^2 + y^3}{x^3 + y^2} = \frac{x^2 + k^3x^3}{x^3 + k^2x^2} =  \frac{k^3x + 1}{x + k^2} = \frac{k^3x + k^5 - k^5 + 1}{x + k^2} = k^3 - \frac{k^5 - 1}{x + k^2} It is clear that  k^5 - 1 = n(x + k^2) for some n. You can take it that  \frac{k^5 - 1}{x+k^2} = 1 so x must be  k^5 - k^2 - 1 and therefore  y = k^6 - k^3 - k
    • 1 follower
    Offline

    ReputationRep:
    (Original post by DeanK22)
    Solution;

    Spoiler:
    Show
    Let y = kx  \Rightarrow \frac{x^2 + y^3}{x^3 + y^2} = \frac{x^2 + k^3x^3}{x^3 + k^2x^2} =  \frac{k^3x + 1}{x + k^2} = \frac{k^3x + k^5 - k^5 + 1}{x + k^2} = k^3 - \frac{k^5 - 1}{x + k^2} It is clear that  k^5 - 1 = n(x + k^2) for some n. You can take it that  \frac{k^5 - 1}{x+k^2} = 1 so x must be  k^5 - k^2 - 1 and therefore  y = k^6 - k^3 - k
    nice. i was at a point of  k^3 -\frac{k^5-1}{x+k^2}
    i didnt really think to let the fraction equal one

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: December 6, 2014
New on TSR

The future of apprenticeships

Join the discussion in the apprenticeships hub!

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