
theorem :: Problem 155
  for x,y,z being positive Nat st
    x / y + y / z + z / x = 3 holds
      x = y & y = z
  proof
    let x,y,z be positive Nat;
    assume
A1: x / y + y / z + z / x = 3;
B2: x / y = y / z & y / z = z / x
    proof
      assume
D1:   x / y <> y / z or y / z <> z / x;
      set a = x / y, b = y / z, c = z / x;
      ((a + b + c) / 3) |^ 3 > a * b * c by SERIES3,D1;
      hence thesis by A1,Multiply1;
    end; then
b1: x / y * y = 1 * y by A1;
    y / z * z = 1 * z by A1,B2;
    hence thesis by b1,XCMPLX_1:87;
  end;
