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**