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sum of two or more nos power of 2.Prove it

Prove that the positive integers that cannot be written as sums of two or more consecutive integers are precisely the powers of 2.

Replies

  • zaveri
    zaveri
    I think 3 is the only number that can be written as the sum of two consecutive positive integers . that is 1 and 2 .
  • Prashanth_p@cchi
    Prashanth_p@cchi
    zaveri
    I think 3 is the only number that can be written as the sum of two consecutive positive integers . that is 1 and 2 .

    There are many..... In fact all, other than the powers of 2.
    Ex:5 can be 2+3, 6 can be 3+2+1.
    whereas 4,8,16 cannot be that way.
  • Prashanth_p@cchi
    Prashanth_p@cchi
    Banashree Patra
    Prove that the positive integers that cannot be written as sums of two or more consecutive integers are precisely the powers of 2.
    How do you want this to be proved???? Examples???
  • Shashank Moghe
    Shashank Moghe
    Banashree Patra
    Prove that the positive integers that cannot be written as sums of two or more consecutive integers are precisely the powers of 2.

    I am curious, is this a textbook example? If you observed that yourself, I need an autograph right away.

    Secondly, it is a real neat one. I am trying, but I kind of know this one needs more than just my pedestrian math skills.

    Thank you for sharing. Do share the source.
  • Shashank Moghe
    Shashank Moghe
    I have been seriously amazed by this mathematical statement. Never thought about this. After some procrastination, today I sat down to write a proof. Hopefully, I have done a convincing job. Please feel free to criticize this. Its handwritten, and my handwriting is very poor. Please accommodate that.
  • Shashank Moghe
    Shashank Moghe
    Shashank Moghe
    I have been seriously amazed by this mathematical statement. Never thought about this. After some procrastination, today I sat down to write a proof. Hopefully, I have done a convincing job. Please feel free to criticize this. Its handwritten, and my handwriting is very poor. Please accommodate that.

    Well, after some deliberation, I found out myself that the "proof" is wrong. It might be a good exercise (to those interested) to find the mistake in the "proof".

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