perplexus.info :: Just Math : A peculiar triplet

A peculiar triplet (Posted on 2016-11-01)

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 |

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

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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