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Thread: Canonical Decomp 2

  1. #1
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    Canonical Decomp 2

    Is there an easy way to approach this number or just start dividing away?

    10,510,100,501
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  2. #2
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    Quote Originally Posted by dwsmith View Post
    Is there an easy way to approach this number or just start dividing away?

    10,510,100,501
    Hint: (x^2+1)^5 = x^{10} + 5x^8 + 10x^6 + 10x^4 + 5x^2 + 1.
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    I am not sure how that is supposed to help, but if I could see the connection, how would I know to come up with (x^2+1)^5?
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  4. #4
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    Quote Originally Posted by dwsmith View Post
    I am not sure how that is supposed to help, but if I could see the connection, how would I know to come up with (x^2+1)^5?
    Second (blatant) hint: Try putting x = 10 in that binomial expansion.

    I have to admit that I cheated in order to find that method. I plugged the number 10510100501 in here in order to find the factors. When I saw the answer I could see why it came out that way.
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