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.
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
Edited on November 3, 2016, 6:15 am