Need to find three integers which can equal Pythagoras' Theorem (a^2+ b^2= C^2) and a+b+c=1000

Have tried with some math logics to solve this problem .
 a^2+ b^2= C^2
 a+b+c=1000

Finally with help of computer solved this problem..

for a in 1..500
  for b in 1..500
    for c in 1..500
      if (a+b+c) == 1000
        if (a*a) +(b*b) == (c*c)
          p a,b,c
          exit
        end
      end
    end
  end
end

Results : 200 ,375 ,425