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.

2,3,5  is the ONLY solution

To prove it :

ab+ac+bc-1 obviously is divisible both by a, b, c and therefore is divisible  by abc   i.e. ab+ac+bc = -1+kabc, k being an integer

divide by abc:    .....   .......

analyze the possible values of k

DRAW CONCLUSIONS

Edited on November 3, 2016, 6:15 am

Posted by Ady TZIDON on 2016-11-02 14:55:51