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Math Help - real number problem 2

  1. #1
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    real number problem 2

    prove that if a positive integer is of the form 6q + 5 then it is in the form 3 q + 2 for some integer q but not conversely.
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  2. #2
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    Quote Originally Posted by saha.subham View Post
    prove that if a positive integer is of the form 6q + 5 then it is in the form 3 q + 2 for some integer q but not conversely.
    This one is easy.
    6q+5=3(2q+1)+2.

    The number 2 is the counterexample needed in the second part.
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  3. #3
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    plzz explain a bit more the part two
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  4. #4
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    Quote Originally Posted by saha.subham View Post
    plzz explain a bit more the part two
    2=3.0+2, so it is of the form 3q+2 (take q=0).

    2 is not of the form 6q+5.
    If it were, then
    2=6q+5
    3=6q
    q=-1/2, which is not an integer.
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