A Math problem related to cryptography

[Jeffery Walker <jeff@beol.net>]

	I have been working on some math and C++ code to implement it. The
problem relates to a possible new means of factoring.  However, I have run
into a problem which I cannot solve. Indeed it maybe impossible. The
problem is this:

	Find and equation using only multiplication, division, GCD, LCM and
powers (not addition or subtraction) in terms of a and b which is equal to
a+b for all Integers.  If so desired it can be assumed that a and b are
relative primes with a>b.  Note that equivalent problems include but aren't
limited to finding a similar equation for a+1. If other functions such as
logs are required they may be allowed but I would have to look into it.

	To encourage people to answer I am offering $20 for a solution and
$10 for a proof that it is impossible.  I will judge all answers as to the
validity both in terms of actually being correct (or in the case of a proof
a valid argument) and in that they do not use functions such as addition or
subtraction which are not allowed.

Thanks,
Jeff
P.S. I am very interested in joining the coderpunks list as I do program
and am interested in cryptography as related to programming.  If someone
would be kind enough to recommend me I thank you.

+____________________________+
|  Jeffery Walker            |
|  E-mail: jeff@beol.net     |
|  http://web.beol.net/jeff  |
+____________________________+