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Math Help - Divisible by 49

  1. #16
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    Quote Originally Posted by Quick
    wouldn't it imply that n+1=k+1???
    Are you familiar with induction?
    If not another excellent thing for you to learn.
    (But first you would have to answer the questions I gave you before we can procede to a new topic).
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  2. #17
    Super Member malaygoel's Avatar
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    a TRY

    I followed TPH's advice and see what I got.
    Let S_n=n^2 + n +2.
    I divide the set of n in two parts:
    One is of the form 7k-4 and second the rest.
    For the first form, you can directly check by substituting the general form 7a-4 for n.
    Now the second case.
    We could see that S_1, S_2,S_4,S_5,S_6,S_7 also satisfy the given condition.
    Now, S_{7+k}=S_k + 7(7+2k+1)
    If you substitute the value of k=1,2,4,5,6,7 you get that S_8.....S_{14} are not divisible by 7.
    Continuing this , now you can substitute the value k=8,9,11,12,13,14 and you get the non-divisibility of next six(out of seven, one you have alredy proved) by 7.
    In this way you can complete the proof by mathamatical induction.

    Bye.
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  3. #18
    MHF Contributor Quick's Avatar
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    Welcome Back

    Hello Malay!
    I thought I wouldn't hear from you for another 6-9 months?
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  4. #19
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Quick
    Hello Malay!
    I thought I wouldn't hear from you for another 6-9 months?
    Even I was thinking the same.
    It is fortunate that there is a computer centre in the college where I can aceess you mhf anytime. Whenever I find time from college studies(which I barely get), I try to visit MHF. Although, by mid october, I will have internet in the room.

    Keep Smiling
    Malay
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