I placed six points on the circumference of a circle such that the distance between any two of the points is an integer. What is the smallest such circle I could use?

What if each distance must be unique?

I think it is impossible with some intuition...but not exactly I can confirm......Placing six point s of Integer coordinates itself may be difficult....In 2D Geometry a circle can be constructed with five points with integer coordinates...But with some intuition I think that the other points that may be found mathematically be some non-integer values or irrational/non-integer rationals I hope