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Math Help - Using this info, factor this number

  1. #1
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    Using this info, factor this number

    880525^2 = 2
    2057202^2 = 3
    648581^2 = 6
    668676^2 = 77
    all (mod 2288233)

    How would I use this info to factor 2288233.
    Now I know I want an x and a y such that x^2 = y^2 mod 2288233.
    So should I be trying to express 77 as a combination of the first 3 equations?
    Unfortunately that isn't of the form y^2, but instead a^2 + b^2 + c^2...
    Looking for any advice.
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  2. #2
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    Mm.. well the product of the first two is 6, which is in the third equation..
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  3. #3
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    yah I though about just using the first 3 equations but Im not getting an answer to factor.

    heres my work:

    (880525 x 2057202) mod 2288233 = 2207120
    so I would add this number to 648581 since 2207120^2 and 648581^2 both = 6mod2288233.
    Now I find the gcd(2855701, 2288233)
    ?

    *after further investigation, 2207120^2 does NOT equal 6 mod 2288233.
    Can someone help me with this?
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  4. #4
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    Quote Originally Posted by chrisc View Post
    yah I though about just using the first 3 equations but Im not getting an answer to factor.

    heres my work:

    (880525 x 2057202) mod 2288233 = 2207120 I suspect that you are on the right lines, and that this last number should actually be 2207124. Then everything seems to work well.
    so I would add this number to 648581 since 2207120^2 and 648581^2 both = 6mod2288233.
    Now I find the gcd(2855701, 2288233)
    ?

    *after further investigation, 2207120^2 does NOT equal 6 mod 2288233.
    Can someone help me with this?
    ..
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  5. #5
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    thank you. so I was able to solve this using only the first 3 equation.
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