Editing Euler brick (section)

== Properties ==

* If {{math|(''a'', ''b'', ''c'')}} is a solution, then {{math|(''ka'', ''kb'', ''kc'')}} is also a solution for any {{math|''k''}}. Consequently, the solutions in [[rational number]]s are all rescalings of integer solutions. Given an Euler brick with edge-lengths {{math|(''a'', ''b'', ''c'')}}, the triple {{math|(''bc'', ''ac'', ''ab'')}} constitutes an Euler brick as well.<ref name=Sierpinski>[[Wacław Sierpiński]], ''[[Pythagorean Triangles]]'', Dover Publications, 2003 (orig. ed. 1962).</ref>{{rp|p. 106}}

* Exactly one edge and two face diagonals of a ''primitive'' Euler brick are odd.

* At least two edges of an Euler brick are divisible by 3.<ref name=Sierpinski/>{{rp|p. 106}}

* At least two edges of an Euler brick are divisible by 4.<ref name=Sierpinski/>{{rp|p. 106}}

* At least one edge of an Euler brick is divisible by 11.<ref name=Sierpinski/>{{rp|p. 106}}