# A Math problem related to cryptography

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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
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: [email protected]     |
|  http://web.beol.net/jeff  |
+____________________________+

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