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

2 Answers

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  • Alan
    Lv 7
    1 month ago

    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 

  • ?
    Lv 7
    1 month ago

    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!

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