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Math Help - Square numbers

  1. #1
    Senior Member Mukilab's Avatar
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    Square numbers

    Could someone give me a method to this question?:

    Rewrite 9991 as the difference of two squares. Use your answer to find the prime factors of 9991.




    Than could someone give me methods to work out any of these annoying square number questions?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Mukilab View Post
    Could someone give me a method to this question?:

    Rewrite 9991 as the difference of two squares. Use your answer to find the prime factors of 9991.




    Than could someone give me methods to work out any of these annoying square number questions?
    As the last digit is a 1 I'm guessing 9 (3^2) is involved). Adding 9 to 9991 gives 10,000 which is also a square number

    9991 = 10,000-9

    10000=100^2
    9 = 3^2

    Rewrite as the difference of two squares
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  3. #3
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by e^(i*pi) View Post
    As the last digit is a 1 I'm guessing 9 (3^2) is involved). Adding 9 to 9991 gives 10,000 which is also a square number

    9991 = 10,000-9

    10000=100^2
    9 = 3^2

    Rewrite as the difference of two squares

    thanks.

    Really cleared a lot up
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  4. #4
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    anothe method :
    let a^2-b^2=9991, then (a-b)(a+b)=9991.
    one of the solution (i think it is a trivial solution) is a-b = 1 and a+b=9991.
    solve it, we get a=4996, and b=4995

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  5. #5
    Senior Member Mukilab's Avatar
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    Truly a fun method!

    Thanks for the help
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