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Math Help - 76x+176y=276

  1. #1
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    76x+176y=276

    76x+176y=276

    76x\equiv 276 \ \mbox{(mod 176)}\Rightarrow 76x\equiv -76 \ \mbox{(mod 176)}\Rightarrow x_0=-1


    176y\equiv 276 \ \mbox{(mod 76)}\Rightarrow 24y\equiv 48 \  \mbox{(mod 76)}\Rightarrow y_0=2

    x=-1+44t

    y=2-19t

    However, this is wrong. Isn't the formula:

    x=x_0+\frac{m}{gcd(76,176)}

    y=y_0-\frac{m}{gcd(76,176)}
    Last edited by dwsmith; November 11th 2010 at 01:50 PM.
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by dwsmith View Post
    76x+176y=276

    76x\equiv 276 \ \mbox{(mod 176)}\Rightarrow 76x\equiv -76 \ \mbox{(mod 176)}\Rightarrow x_0=-1


    176y\equiv 276 \ \mbox{(mod 76)}\Rightarrow 24y\equiv 48 \  \mbox{(mod 76)}\Rightarrow y_0=2

    x=-1+69t

    y=2-69t

    However, this is wrong. Isn't the formula:

    x=x_0+\frac{m}{gcd(76,176)}

    y=y_0-\frac{m}{gcd(76,176)}
    It works out with

    x=x_0+\left(\frac{176}{gcd(76,176)}\right)t

    y=y_0-\left(\frac{76}{gcd(76,176)}\right)t
    Last edited by undefined; July 16th 2010 at 06:09 PM. Reason: added "t"
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