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.
Show that no other exist.
(In reply to re(2): The triple without complete proof
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.