rsa-membership.pdf error in proof

[ldgarratt]

The proof is wrong. It says:

wlog p < q so
(p+q)/pq <= 2q/qq

This is not correct:
E.g. take p = 3, q = 7 we get 0.476 < 0.226

To overestimate the size, the numerator should be as large as possible (2q) and the denominator should be as small as possible (p^2).

The theorem is still obviously true though.

I'm not sure a formal proof is necessary as the result is quite intuitive, but here is my attempt:

Proof:
(p+q)/pq = p/pq + q/pq = 1/q + 1/p.
Both terms tend to 0 as p and q tend to infinity.

Happy to do a pull request if you give me the .tex code.

I did quite like the proof by security reduction though :)