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Math Help - Direct Proof

  1. #1
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    Direct Proof

    If x is an odd integer and y is an odd integer then xy is an odd integer. Use direct proof to prove the following.

    I am stumped on where to go from here. All I know is that the definition of an odd integer is n=2k+1 where n is the integer.

    So I assume that I need x=2n+1 and y=2m+1 but I really don't know where to go from here. This seems really simple but where to start is stubborn to me.
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  2. #2
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    Hello,
    Quote Originally Posted by premierplayer View Post
    If x is an odd integer and y is an odd integer then xy is an odd integer. Use direct proof to prove the following.

    I am stumped on where to go from here. All I know is that the definition of an odd integer is n=2k+1 where n is the integer.

    So I assume that I need x=2n+1 and y=2m+1 but I really don't know where to go from here. This seems really simple but where to start is stubborn to me.
    Then xy=(2n+1)(2m+1)=4mn+...
    expand and see if it can be written in the form 2k+1, for some integer k
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hello,

    Then xy=(2n+1)(2m+1)=4mn+...
    expand and see if it can be written in the form 2k+1, for some integer k
    xy=(2n+1)(2m+1)=4mn+2 because of distributive property?
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  4. #4
    Moo
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    Quote Originally Posted by premierplayer View Post
    xy=(2n+1)(2m+1)=4mn+2 because of distributive property?
    Is it university level ?

    read this : FOIL rule - Wikipedia, the free encyclopedia
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  5. #5
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    Yeah it is, its just I haven't taken a math class in like 5 years. Go me.
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  6. #6
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    ok so I foiled the following...

    4nm+2n+2m+1

    I am now sure where to go from here tho.
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  7. #7
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    ok so ive been working on this..

    x= 2n+1 y=2m+1

    xy= (2n+1)(2m)+1

    xy= 4nm +2n +2m +1 using FOIL

    2(nm+n+m) +1 using factoring by 2

    n & m are real numbers so...

    nm + n + m = k (real number) using addition/multiplication of real numbers

    2k+1 is the same as the definition of odd number...

    is this right? Can anyone add to this.
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  8. #8
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    Yes, that works. It is a bit long.
    Note that an even number plus one is odd.
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