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

STEP Maths Question

Announcements Posted on
Have you had the experience of living with an eating disorder? Share your story here.. 06-03-2015
ISA/EMPA exam discussion on TSR 05-03-2015
  1. Offline

    Please refer to Advanced Problems in Core Mathematics by Stephen Siklos, page 24 (question 24, part iii) here.

    Now that we know n and a are both even, we can follow the method used in part (ii) and set n = 2m and a = 2b . This gives
    (2m − 2b)^3 + (2m)^3 = (2m + 2b)^3
    from which a factor of 2^3 can be cancelled from each term. Thus m and b satisfy the same equation as n and a. They are therefore both even and we can repeat the process.
    Repeating the process again and again will eventually result in an integer that is odd which will therefore not satisfy the equation that it is supposed to satisfy: a contradiction. There is therefore no integer n that satisfies the equation
    I repeated the process once by taking out the factor 2^3 from the equation, giving (m-b)^3 + m^3 = (m+b)^3, where m and b are both even/odd. So how am I supposed so obtain "integer that is odd which will therefore not satisfy the equation"? If both m and b are even, it will result in a repetition of part ii, which consequently results in part i, while b being odd will result in part i right away.

    So... how do I justify the bold statement above? Thank you!
  2. Offline

  3. Offline

    If you keep dividing by two you eventually get an odd number.
  4. Offline

    Considering m in terms of prime factors should help you see why it works.
  5. Offline

    (Original post by Zuzuzu)
    Considering m in terms of prime factors should help you see why it works.
    Could you please elaborate? Thank you.
  6. Offline

    (Original post by johnconnor92)
    Could you please elaborate? Thank you.
    m = 2^n \cdot \text{(at least one odd prime)}

    Repeated division by 2 should give you an odd number eventually.


Submit reply


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: May 21, 2012
2015 general election
New on TSR

Ask a Lib Dem MP your questions

Grill Norman Lamb MP about mental health

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