Can 169,173 be represented as a sum of 2 squares?

169173

factor are 1,3,3, 18797

 since 3 is the only double factor

we take :

= 9*( 18797)

since 138^2 = 19044

now try all squares

from 0 to 137

and determine if the 2nd number is also a square

thats

18797 = (x^2 +y^2)

y^2 = 18797 - x^2

now , try x from 0 to 137

looking for value of y^2 where you

have an integer square root

x = 29 and

y = 134

now, you know

169173 = 9*( 29^2 + 134^2)

169173 = 3^2*29^2 +3^2(134)^2

169173 = 87^2 + 402^2

so 87 and 402 

Yes it can...

Now, can you find them?

There are many ways/tricks, and simplifications of  "?" tactic/answer.

As in, the search for √(n/2) max trick. 

And then mod 2 or 4 reduces further the search. 

You can reduce it to about 40 numbers to try!