# Does the sum of the digits tell us anything about the relation between these two functions

The number $K$ is expressible as part of one of either of two quadratic functions with integer coefficients. One of the functions is quadratic in $\pi$ and one is quadratic in $e$:

$$1955e^2+223e-2383=eK$$

$$-134\pi^2+5842\pi-2389=\pi K$$

The sum of the digits of all the coefficients in the first equation is 11. In the second equation this sum is -11. (When summing take into account the sign on the coefficient). Is this just a coincidence or does it point to some special relation?

-
Those polynomials are quadratic in $\pi$ and $\mathrm e$, not cubic. – joriki Sep 19 '12 at 21:27
Oops. Duly edited. – ben Sep 19 '12 at 21:30

The two numbers defined by these two equations are not the same. As calculated by Wolfram|Alpha, the first is $4660.58426632588638\ldots$ whereas the second is $4660.58426632589179\ldots$ .
Wouldn't we expect $e$ and $\pi$ to be algebraically independent? It is a very close match, though. – Ross Millikan Sep 19 '12 at 21:56