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
The triple without complete proof by Jer)
The (2,3,5) is the only one found by
For tot = 6 To 1000
For a = 1 To tot / 3
For b = a + 1 To (tot  a) / 2
c = tot  a  b
DoEvents
If (a * b) Mod c = 1 Then
If (b * c) Mod a = 1 Then
If (a * c) Mod b = 1 Then
Text1.Text = Text1.Text & a & Str(b) & Str(c) & crlf
End If
End If
End If
Next
Next
Next tot
for numbers totaling no more than 1000. The program of course listed them in ascending order.

Posted by Charlie
on 20161101 13:40:17 