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

Banashree Patra

Banashree Patra

@banashree-patra-m0OJwR • Oct 25, 2024
Prove that the positive integers that cannot be written as sums of two or more consecutive integers are precisely the powers of 2.
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  • zaveri

    zaveri

    @zaveri-5TD6Sk • May 17, 2012

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

    Prashanth_p@cchi

    @prashanth-p-at-cchi-rg0z63 • May 23, 2012

    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.
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  • Prashanth_p@cchi

    Prashanth_p@cchi

    @prashanth-p-at-cchi-rg0z63 • May 24, 2012

    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???
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  • Shashank Moghe

    Shashank Moghe

    @shashank-94ap1q • Sep 17, 2014

    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.
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  • Shashank Moghe

    Shashank Moghe

    @shashank-94ap1q • Jan 6, 2015

    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.
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  • Shashank Moghe

    Shashank Moghe

    @shashank-94ap1q • Jan 8, 2015

    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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