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A peculiar triplet (Posted on 2016-11-01) Difficulty: 3 of 5
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.

See The Solution Submitted by Ady TZIDON    
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re: The triple without complete proof | Comment 2 of 7 |
(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 2016-11-01 13:40:17
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