This triplet of positive integers has this peculiarity:

A product of any its two numbers divided by the 3rd number

has 1 as a remainder.

Find it.

Show that no other exist.

(In reply to

re(2): The triple without complete proof by Charlie)

if there were duplicates like a,a,b then

* two numbers divided by the 3rd number e.g.* a*b/a would never leave a remainder - you do not need computer to tell you this.