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Lv 7
? asked in Science & MathematicsMathematics · 3 weeks ago

What are the 2 representations of the number 169,713?

169713 has 2 representations as a sum of 2 squares.

2 Answers

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  • Alan
    Lv 7
    3 weeks ago
    Favourite answer

    By the same method as you previous question 

    prime factor are 3^2 × 109 × 173  

    so 3 is only double factor 

    9(18857) = 3^2 (x^2 + y^2)  

    since square root of 18857 =  137.3207923 

    x and y must be less than  138 

    so try all values between 0 and 137 for x 

    and check if y is an integer  

    x^2 + y^2  =  18857 

    y^2 = 18857- x^2  

    (then check if square root of y^2 is an integer  

    I get 19 and 136 for  square factor of  18857 

    and 59 and 124  

    so you have 

    3^2( 19^2  + 136^2)  

    (3*19)^2    + (3*136)^2  

    (57)^2  + 408^2 = 

    so you have 

    3^2( 59^2 + 124^2)  

    ( (3*59)^2   + (3*124)^ 2  ) 

    so (177^2  +  372^2  ) =  169713 

    (57)^2 + 408^2    

    and 

    (177^2 + 372^2 ) =  

  • 3 weeks ago

    It has no representations. You have it mixed 

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