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

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 ) =  

It has no representations. You have it mixed