Property of Symmetry Basic

Video tutorial

Lecture Notes

Most indeterminate equations are symmetric. This means that swaping its variables (e.g. $x$, $y$, etc) does not change the nature of the given equation. Such a symmetry property offers some benefits for us to exploit:

  • Quite often, we just need to find all the "distinct" solutions and simply say their permutations are all valid solutions.
  • More usefully, we can always assume an order of all the variables (e.g. $x \ge y \ge z \ge \cdots$). As we will see soon in the next couple of lessons, such an assumption plays a key role in employing the squeeze method.

Assignment >>>