Exponentiate In Pairs, Get Numbers (Posted on 2007-06-08)

	Submitted by K Sengupta
Rating: 4.0000 (1 votes)
Solution:	(Hide)
When a =1, then: ab = c, gives b=c, while ca=b gives c= b. Thus, b=c=a, so that (a,b,c) =(1, 1, 1). When a>1, we have c = ab> 1 and b = ca > 1. Now, c = ab > a; while a = bc > b, so that c> b. But, b= ca> c. This is a contradiction. When a< 1, we have c, b < 1. Now, c = ab < a; while a = bc < b, so that c< b. But, b= ca< c. This is a contradiction. Combining the three cases, (a,b,c) = (1,1,1) is the only possible solution to the given problem.

	Subject	Author	Date
	Another solution	Gamer	2007-06-08 23:53:55
	re(3): Cyclical	brianjn	2007-06-08 21:14:52
	re(2): Cyclical	Robby Goetschalckx	2007-06-08 09:54:37
	re: Cyclical	brianjn	2007-06-08 09:35:25
	Cyclical	brianjn	2007-06-08 09:32:59
	Proof	Old Original Oskar!	2007-06-08 09:31:56